Here are algorithms for cubes 5x5x5, 7x7x7, 9x9x9 etc. These tips aren't especially original, but are collected together for ease of use as I tend to forget them if not cubing regularly. I use simple easy-to-remember beginners' methods throughout my cubing. The general way to solve any large cube is:
Each centre is 3x3, 9-cubie-faces. Move some of the 3x1 bars around between these two faces (only!) until you have a small number of corner pieces and edge pieces remaining to fix. Then use the following as needed:
In this case, each centre has one cubie face of the wrong colour in the corner. Rotate the Upper face and the Front face so that the Front-face-coloured cubie is in the bottom-right position of the Upper face, and the Upper-face-coloured cubie is in the upper-right position of the Front face. Making all adjustments on the right column only, this could be written as uuf/uff. The algo to solve this situation is
Each centre is 5x5, 25-cubie-faces.
First, solve the centremost 3x3 section of 9 cubie faces. You will be moving some 5x1 bars around, but will only be interested in the middle 3 of the 5 cubies in each bar. Use the same algos as the 5x5x5 cube final two centres section above.
Now address the outermost ring. Move some of the 5x1 bars around between these two faces until you have a small number of corner pieces and edge pieces remaining to fix. Rotate the centres as needed so you are only working on the rightmost column of the Upper face and the Front face.
Each centre is 7x7, 49-cubie-faces.
First, solve the centremost 3x3 sections (9 cubie faces). Use the same algos as the 5x5x5 cube final two centres section above.
Now solve the next-outermost rings exactly the same as with the 7x7x7 cube.
Finally solve the outermost rings. Rotate the centres as needed so you are only working on the rightmost column of the Upper face and the Front face.
If one edge has a green/yellow (green on up face) centre piece, and a left wing-piece is green/yellow while the matching right wing-piece is yellow-green, the left wing-piece is correct and the right one needs to be flipped at some point. This is true for any size odd-numbered cube.
I solve almost all edges by the same method. On a 5x5x5 cube:
If the non-paired wing piece is in the RB position of the UR edge, then use FR'F'. Similarly for the down L/R edges. Sometimes you'll need to reverse the edge with a non-matched pair, using (for a LU edge) something like U'F'L'U and maybe more. It's a good idea to use the full Flipping Algo below each time (without the single slice moves disrupting the centres), not so much because all 7 moves are always needed, but because it both saves thinking how many are needed and also helps to memorise the full algo for when it is needed.
Nearing the end of solving the edges, with three edges remaining set them up as above and either the three will solve all at once or there is a parity problem. Fix the parity problem, solve edges as usual until three left, then set them up as above. If you end up with only two unsolved edges, only in that case would you need to use the flipping algo.
This flips the entire edge, leaving everything else the same.
Use it by first rotating a slice to match a pair, use the flipping algo on that paired edge, then unrotate the slice to make the centres whole again and the edges should now all be solved.
Personally I have hardly been using this algo at all, finding it difficult to match the correct slices on cubes larger than 5x5x5. However, I shall use it more now for simple edge reversals without needing to make pairs.
All can be solved with (L'U2)x5. Use (LU2)x5 or (RU2)x5 etc if you prefer. The U2 involves the single face only. For the L':
5x5x5 cube: L' of outside left face + adjacent left slice
7x7x7 cube: 5x5x5 cube parity; and L' of outside left face + 2 adjacent left slices
9x9x9 cube: 7x7x7 cube parities; and L' of outside left face + 3 adjacent left slices
Etc
So a 5x5x5 solve may have 0 or 1 parity problems, a 7x7x7 solve may have 0 or 1 or 2 parity problems, a 9x9x9 solve may have 0 or 1 or 2 or 3 parity problems, and so on, all fixed by the simple (L'U2)x5 algo on 1, 2, 3 etc slices as needed.
To keep it simple, if doing a 7x7x7 cube I would match up all the outer wings first, fixing that parity if needed. At this point, the "outer wings" are all paired up, so it is like solving the edges on a 5x5x5 cube, where there may be the second parity problem. Similarly for a 9x9x9 cube, where the outer wings are first paired up and then tripled up, with the triple having its own possible parity problem.
Solve in exactly the same way as above, simply extending the methods as needed.
