The only thing new needed for 5x5 is a way to solve the +Centers (the X-Centers can be solved using the 4x4 sequences as shown here). The first step to solving the +Centers is to eliminate those that are are quarter-twisted, but before getting into that first look at sequences that fix pairs of half-twisted centers using slightly modified versions of the 3x3 Supercube Sequences.

On the first cube below the sequence fixes a pair of half-twisted +Centers on the front face and another pair on the top face. On the second cube the two pairs are vertical instead of horizontal. The third cube has a horizontal pair on the front face and a vertical pair on the top face. The fourth cube has the second pair on the back face. The fifth cube has both pairs on the front face.

The following shows how a slightly modified version of the sequence from the first cube at the top of the page can be used to eliminate +Centers that are quarter-twisted as shown on the front face of the cubes below. On the first cube, the first three moves put the counter-clockwise piece in the proper position then the sequence is applied, the last three moves undo the first three. The third and fourth moves cancel each other so they can be eliminated and as shown on the second cube. This sequence also results in two centers on the top face being half-twisted but that does not matter because at this point the goal is just to eliminate quarter-twisted centers.

To use this sequence it is only necessary that there are two +Centers with quarter-twisted arrows in the locations shown on the front face. The direction of the arrows does not have to match the setup nor do the rest of the arrows on the face. The quarter-twisted centers will either be solved or half-twisted (as in no longer quarter-twisted) as a result of the sequence.

The following shows how the above sequence is used to eliminate quarter-twisted +Centers on all faces. In the table below the cube, "Make Setup" means to turn the cube so that there are two quarter-twisted centers in the locations shown on the above cube.

Complete the solve by using the sequences for half-twisted +Centers. First use the one that fixes all four centers on the front face (moves 1-18). Turn the cube to move the Orange face to the front and do it again (19-37). Turn the cube so the last two pairs are on the top and front faces and then do the sequence to fix them (38-51). The last move turns the cube to the home position (all arrows point up).

You can try using the above sequences to solve 5x5 Supercubes With Random +Centers.