The 5 by 5 by 5 Rubik's Cube (also called the Professor's cube) solves similarly to the 4 by 4, although the centers on this puzzle are fixed to the core and cannot move around. The link below will show you how to solve the cube. The Professor's Cube was invented by Udo Krell (I don't know what year), and all 5 by 5 mechanisms are unique.
5 by 5 Solution