Reduction method: centres (4 kinds of pieces), edges (inner pairs, then outer wings), like a 3x3 + parities. Full course with animations and simulator: strefa-kostek.pl/en/kursy
R U F… - one outer layer, quarter turn clockwise, looking at that face. 2R / 3R = only the second / third layer from the right (direction as R), Uw Dw = two layers, 3Rw 3Uw = three layers (half the cube), (2R2 3R2) = both inner layers together. Order: centres → inner pairs (like 4x4) → outer wings (like 5x5) → like a 3x3 + 4x4 parities.
Left diagram: top (back at the top), right: front; yellow = colour being built. Turn F so that the piece is in the circle, and U so that the spot in the circle is free. The algorithm changes only that spot on top.
3Rw' D2 3Rw left half of the bottom ↔ right half of the front (from the bottom to the front; only while the bottom is not solved). Another side to the front: y.
Check: white on the bottom, green at the front - red on the left. Swap top↔front: (3Rw U2 3Rw') F2 U2 (3Rw U2 3Rw'); red↔orange: z, alg, x2, alg, x.
The two middle wings of each edge together (like 4x4).
Inner pair = the midge from the 5x5.
Only Uw / Dw (two layers). The right edge must not be finished.
Outer wings swapped. Edge at the top front:
2R2 B2 U2 2L U2
2R' U2 2R U2 F2
2R F2 2L' B2 2R2
Yellow on top, outer moves only. Algorithms: 3x3 cheat sheet.
1 or 3 yellow edges (edge without yellow at the front):
3Rw U2 x 3Rw U2 3Rw U2 3Rw' U2
3Lw U2 3Rw' U2 3Rw U2 3Rw' U2 3Rw'
Exactly 2 corners in place:
(2R2 3R2) U2 (2R2 3R2) 3Uw2
(2R2 3R2) 3Uw2, then yellow edges again.