How to Solve a 5x5 Cube - Step-by-Step Course

Before You Start

This course assumes you can already solve a 3x3 cube - even with the course in front of you. If not yet, start with the 3x3 cube course, because its algorithms come back here in stage 7. If you already know the 4x4 course, you will recognise some of the moves straight away - but the 4x4 is not required. You can turn the animations in this course: drag the cube with your finger or mouse.

What a 5x5 cube is made of

The 5x5 cube has 8 corners - the same as on a 3x3. The rest is divided into smaller pieces:

• Centres - a 3x3 square on every face, i.e. 9 pieces. In the very middle is the fixed centre: it never changes position, just like the centre of a 3x3 cube, and it tells you what colour the face is. Next to it are four t-centres (together with the fixed centre they form a small cross), and in the corners of the square four x-centres.
• Edges - each made of three pieces: the midge (middle edge piece) and two wings on its sides. The midge behaves like an edge on a 3x3, while the wings get spread all over the cube when you scramble.

The reduction method

First you solve the face centres, then you join the pieces of each edge into threes. After that every 3x3 square works like a centre of a 3x3 cube and every group of three like one of its edges - the cube behaves like a 3x3 and you solve the rest with a method you know. This is called reduction (reducing a 5x5 to a 3x3):

1. centres - stages 2-4,
2. edges - stages 5 and 6,
3. continue like a 3x3 - stage 7.

Two pieces of good news for those who know the 4x4: the fixed centres set the face colours by themselves, so you cannot build the centres in the wrong order, and the 3x3 part has no surprises at all - the only parity waits at the last edge.

1Move Notation

The letters R, L, U, D, F, B mean the same as on a 3x3 cube: a quarter turn of the right, left, up, down, front and back face clockwise, when you look straight at that face. An apostrophe means a turn the other way, and a two - a half turn. On a 5x5 each such letter turns only one, outer layer. Two new kinds of moves are added:

• 2R - only the second layer from the right, without the outer one. The same goes for 2L - the second layer from the left.
• Uw - the two top layers at once (w for “wide”). The same goes for Dw - the two bottom layers.

The direction is the same as the ordinary move of that face: 2R turns the same way as R, and Dw - like D, i.e. clockwise when you look at the cube from below. You do not turn the middle layer (the one with the fixed centres) in this course. Click a move below to see it on the cube:

x, y and z are rotations of the whole cube in your hands, as on a 3x3: x like the R move (the front goes to the top), y like the U move (the right face goes to the front), z like the F move (the top goes to the right).

The most important sequence in this part of the course is 2R U 2R': second layer up, top to the left, second layer down. It takes two pieces from the right column of the front centre to the top, and the second layer goes back to its place.

2White Centre

Goal: nine white centre pieces on the face with the fixed white centre. Edges and corners do not matter yet.

Turn the cube so that the fixed white centre is on top - that is where you build the white square. You build the centres in two steps: first the cross (t-centres), then the x-centres. In the animations only the white centre pieces are coloured, the rest is greyed out.

Step 1: the cross

You insert every white t-centre from the front to the top with the same move:

1. Turn the top (U) so that the back t-centre of the top (the one furthest from you) is free - not white.
2. Turn the front (F) so that the white t-centre is in the right t-centre position of the front - just to the right of the fixed centre.
3. Do 2R U 2R'.

The white t-centre jumps to the top, and the white t-centres that were already there stay on it - after each time there is one more. The x-centres jump between the top and the front along the way, but in this step do not pay any attention to them.

When there is no white t-centre on the front

• The white t-centre is on another side - rotate the whole cube (y) so that this side is at the front. The fixed white centre stays on top.
• The white t-centre is on the bottom - turn the bottom (D) so that it is in the left t-centre position of the bottom (next to the left face), and do 2R' D2 2R. The left column of the bottom swaps with the right column of the front, so the t-centre lands straight in the right t-centre position of the front, and the top stays untouched. Then you insert it as usual.

Step 2: x-centres

When the cross is done, you insert the white x-centres. The move 2R U 2R' would take the back t-centre off the top, so here you use a longer sequence that does not touch the cross:

1. Turn the top (U) so that the front-right x-centre of the top centre (closest to you, on the right) is free.
2. Turn the front (F) so that the white x-centre is in the top-right corner of the front centre - right below the free spot.
3. Do 2R U 2R' U 2R U2 2R'.

The sequence is easy to remember: it is the familiar 2R U 2R', then U and the same thing again with U2 in the middle. The white x-centre goes to the top, and the cross and the other x-centres stay in place.

When there is no white x-centre on the front - same as with the t-centres: from a side, rotate the cube (y), and from the bottom, turn the bottom (D) so that the white x-centre is in the left column of the bottom, and do 2R' D2 2R. The x-centre ends up in the right column of the front - turn the front (F) so that it is in the top-right corner.

3Yellow Centre

Goal: nine yellow centre pieces on the face with the fixed yellow centre - opposite the white ones.

Turn the cube with the white centre on the bottom (x2). The fixed yellow centre is now on top. You build the yellow centre exactly like the white one: first the cross (free back t-centre on the top, yellow one in the right t-centre position of the front, 2R U 2R'), then the x-centres (free front-right x-centre on the top, yellow one below it, 2R U 2R' U 2R U2 2R').

The white centre on the bottom is safe: 2R briefly moves its right column to the front, but 2R' immediately puts it back. Yellow centre pieces can now only be on the top and on the sides (the bottom is already full of white), so you only need to rotate the cube (y) to bring the side with yellow to the front. 2R' D2 2R is not needed in this stage - it would break the white centre.

4The Last Four Centres

Goal: all six centres done.

How to hold the cube

Rotate the cube (z) so that white is on the left and yellow on the right. The remaining four centres now lie on a “ring” around the cube: top, front, bottom and back. You use the same moves as before - 2R U 2R', 2R U 2R' U 2R U2 2R' and 2R' D2 2R do not touch the left and right centres. Instead of a y rotation (which would bring white to the front) you rotate the cube with x, and to swap the front with the back - with y2 (white and yellow then swap sides, but stay on the sides).

The colour order takes care of itself: you build each colour around its fixed centre. This stage is three centres in a row - the fourth solves itself.

The first ring centre

Build the centre on top - in the colour of its fixed centre. Pieces of that colour can be at the front (you insert them straight away), on the bottom (2R' D2 2R) or at the back (y2 - the back goes to the front).

The second and third

Move the finished centre to the back: rotate the cube (x) - the front goes to the top, and the top to the back. On top, build the next centre in the colour of its fixed centre. You take the pieces from the front or from the bottom (2R' D2 2R). Do not bring the back to the front any more (no y2) - the finished centre is there.

After the second centre, rotate the cube (x) again. Now the centres at the back and on the bottom are done, and the two unsolved ones are on the top and at the front. Build the top one, taking pieces only from the front. When the top is done, only one colour is left at the front - the last centre solves itself.

5Edges

Goal: in each of the 12 edge positions the midge and two wings with the same colours - on every face the edge looks like a single colour. The centres stay solved.

You build an edge around its midge: you add one wing to it at a time. All the moves in this stage (apart from the algorithms) turn only the outer layers or the whole cube, so they do not break the centres or finished edges.

1. Rotate the whole cube so that an unsolved edge is at the front left (vertical, between the front and the left face). Look at its midge: what colour it has at the front (e.g. green) and what colour on the side (e.g. red).
2. Find a wing with the same two colours that is not yet next to the midge, and bring it to the front-right edge with moves that do not touch the left edge:
   • from the top: turn the top (U) until it is on the right side of the top, and do R',
   • from the bottom: turn the bottom (D) until it is on the right side of the bottom, and do R,
   • from the back right: R2, from the back left: B2 and R2.
3. Look at the front colour of the wing. If it is not the same as the front colour of the midge, do R U R' F R' F' R - the right edge flips, the wing moves to its other end and shows the correct colour at the front.
4. Now the front colour matches. The wing is:
   • at the bottom of the right edge - do Uw' R U R' F R' F' R Uw, the wing goes to the top of the left edge,
   • at the top of the right edge - do Dw R U R' F R' F' R Dw', the wing goes to the bottom of the left edge.

Repeat steps 2-4 for the second wing - the front-left edge is done. Then rotate the cube so that the next unsolved edge is at the front left, and so on. A wing that is once correctly placed next to the midge will not move again - the algorithm only changes the spot in the left edge where the new wing goes.

How it works: Uw' moves the upper rows of the sides one face to the right, so the upper wing of the left edge moves away to the right. R U R' F R' F' R flips the right edge - your wing moves from the bottom to the top. Uw moves the upper rows back and takes it with them to the top of the left edge, next to the midge. The Dw version does the same for the lower wing.

The wing is in the same left edge

Sometimes the missing wing is already in the left edge, but at the wrong end - you can tell because it shows its colours the other way round compared with the midge. You have to take it out of there: bring any unsolved edge to the right (as in step 2), and then do the algorithm - Uw' R U R' F R' F' R Uw when the wrong wing is at the top of the left edge, or the Dw version when it is at the bottom. The wing moves to the right side and you carry on as usual.

Note: the front-right edge must not be finished when you do the algorithm - it would break apart. In the normal steps it never is, because a foreign wing sits in it.

6The Last Edge

Goal: all 12 edges done.

In roughly every other solve, at the end you are left with one edge in which both wings are swapped: on each side you see the pattern “colour - other colour - colour”, because the wings show their colours the other way round compared with the midge. You cannot fix this with the steps from stage 5 - swapping with another edge always breaks that one. Speedcubers call this parity. It is not a mistake in your solving, just the way the wings happened to be joined.

Turn the cube so that this edge is at the top front (horizontal, between the top and the front), and do:

2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2

The algorithm has 15 moves, but a simple rhythm: you turn only the second layers (2R, 2L) and the outer faces by half turns. It swaps both wings of the top-front edge and changes nothing else - the centres return to their place, and finished edges stay finished.

Watch the direction of 2L: it turns like L, i.e. clockwise when you look at the left face - the opposite way to 2R.

7Continue Like a 3x3

Goal: a solved cube.

The centres and edges are done, so the cube behaves like a 3x3: a 3x3 square is a centre, a group of three pieces is an edge. Solve it with the method from the 3x3 cube course (yellow on top): daisy, white cross, white corners, second layer, yellow cross, yellow edges, corners into place and corner twisting.

Use only outer-layer moves (R, U, F, L, D, B) and whole-cube rotations. Moves like Uw, Dw or 2R would break the centres and edges.

Unlike on the 4x4, on the 5x5 you will not get any parity here: the fixed centres and the midges behave exactly like a 3x3 cube, so all the cases from the 3x3 course look the same. If something does not match (e.g. 1 or 3 edges in the yellow cross), it is a sign that one of the edges was not paired correctly - go back to stage 5.

Done - the 5x5 cube is solved. The first solves will take quite a while, but after a few times the centres and edges will start to flow.

Cheat Sheet: All Algorithms

Everything you need to remember in one place. The stage 7 algorithms are in the 3x3 course cheat sheet.

Printable cheat sheet (A4 / PDF)

1. T-centre - free back t-centre on the top, t-centre in the right t-centre position of the front: 2R U 2R'.
2. X-centre - free front-right x-centre on the top, x-centre in the top-right corner of the front: 2R U 2R' U 2R U2 2R'.
3. From the bottom to the front - piece in the left column of the bottom: 2R' D2 2R (only while the bottom is not solved yet).
4. Centre order - white on top, x2 and yellow, z (white on the left) and the three ring centres, with x between them. Face colour = its fixed centre.
5. Edges - midge at the front left, wing at the front right, the same colour at the front (otherwise first R U R' F R' F' R). Wing at the bottom: Uw' R U R' F R' F' R Uw, at the top: Dw R U R' F R' F' R Dw'.
6. Last edge with swapped wings, at the top front: 2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2.

Solve It Yourself

A practice simulator. You can scramble the whole cube or choose a stage - then you get a random cube with the previous stages solved. You turn an inner layer by dragging a sticker in the second row, or with the 2R and 2L buttons.

Common Problems

I did an algorithm and it is worse than before

The most common cause on a 5x5 is mixing up layers: 2R turns only the second layer, Uw the two top ones at once, and R only the outer one. The second - direction: 2L, Dw and D, just like L, count as “clockwise” looking at that face (go back to stage 1 and click these moves). Do the algorithm slowly, move by move along with the animation, and do not stop halfway.

When inserting, a piece that was already on top escapes

For t-centres the back t-centre of the top must be free, and for x-centres - the front-right x-centre. Before the algorithm always turn the top so that this spot is empty. X-centres escaping during the cross step are nothing to worry about - in that step only the t-centres count.

Inserting an x-centre breaks the cross

For x-centres you use the longer sequence 2R U 2R' U 2R U2 2R'. 2R U 2R' on its own takes the back t-centre off the top. Also check the second move: it is U, and in the second part U2.

After the stage 5 algorithm the centres are scattered

The Uw (or Dw') at the end was missing, or one layer was turned instead of two. Uw and Dw must turn two layers together - the middle layer stays in place.

A finished edge broke apart

The front-right edge was finished when you did the algorithm. First bring a wing (or any unsolved edge) there - see stage 5.

The last edge will not pair up

This is the parity from stage 6: both wings of the last edge are swapped. Put it at the top front and do the algorithm from stage 6.

The cube locks up when turning an inner layer

Before a 2R or Uw turn the other layers must be aligned, otherwise the pieces catch on each other. Magnetic cubes align the layers by themselves and make learning much easier. See 5x5 cubes.

How long does it take to learn?

If you can solve a 3x3, there are only a few new things: three moves for the centres, two for the edges and one for the parity. Most people solve the 5x5 with the course after three or four evenings. This method needs around 700 moves, so at first a solve takes 20-30 minutes, but with practice it drops below 10 minutes.

What Next?

Once you can solve the cube a few times without looking at the course, start timing yourself. You will gain the most on the centres and edges:

• Bars instead of single pieces - make a bar of a t-centre and two x-centres in the right column of the front centre, turn the top so that its left column is free, and insert the bar at once: 2R U2 2R' swaps the left column of the top with the right column of the front.
• Several edges at once - advanced solvers pair wings “on the fly”, without an algorithm for each one (the freeslice method).
• The Yau method - the most popular among competitors: first two centres, then three edges of the white cross, then the rest of the centres and edges. The cross is built along the way, so the 3x3 part is shorter.
• Bigger cubes - the 6x6 and 7x7 are solved with the same reduction: centres, edges, like a 3x3.