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First fix the center planes; the first 2 opposite, then adjacent. Then fix the edges (excl. corners). After that the big cubes behave like the standard 3x3.

Last 2 center planes: Hold the 2 unfixed planes in front of you (F and U planes), Mirror the below cells in the F/U edge:

To switch the right cross cells: Rw' F' Lw' Rw U Rw U' Lw Rw'

To switch the lower right point cell on the up plane with the upper right point cell of the front plane: Rw U Rw' U Rw U2 Rw'

To fix the edges, hold the edge cells on both left/right sides to your front plane. They should not face with the same color when on opposite sides: To re-orient the cells: L' U' R F' R'

For the last 2 edges: ©CubeSkills

General solving of 5x5 cube: ©Noah Richardson