The X-Centers on the 5x5 Supercube are solved the same way as the 4x4 Supercube. The following shows a comparison of the 4x4 and 5x5 cubes for the sequence which is used to get all centers on each face pointing in the same direction.
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The final step of solving pairs of faces by twisting all four X-Centers on
each face as one is also done with the same sequences as the 4x4 cube (which
are the same as the 3x3 cube).
However, if at the end of a solve there remains a single face with all four
X-Centers half-twisted then the procedure is a bit different.
To half-twist all four X-Centers on a single face, first use the
3x3 Supercube Sequence to half-twist
all of the centers on the top face including the +Centers and Fixed Center
(moves 1-12 on the cube below).
At that point, the X-Centers are fixed but the +Centers and Fixed Center
are half-twisted so turn the cube so the twisted centers are on the front
face and use the sequence to half-twist just the +Centers (14-29).
Finally, turn the cube so the twisted centers are on the top face and use the
sequence to half-twist all the centers again but this time twist two layers
together on each move so that only the Fixed Center is twisted (30-42).
The following shows another way to do the same thing as above. This uses the sequence shown on the second cube at the top of the page (moves 1-22 on the cube below). The sequence is repeated (23-44) to complete the solve of the four half-twisted X-centers on the top face.