The 5x5x5 or Professor's Cube is a 3-D combination puzzle, a 5×5×5 version of the original Rubik's Cube. It has qualities in common with both the 3×3×3 Rubik's Cube and the 4×4×4 Rubik's Revenge, and solution strategies for both can be applied to the Professor's Cube.

The Professor's cube was invented by Udo Krell in 1981. Out of the many designs that were proposed, Udo Krell's design was the first 5×5×5 design that was manufactured and sold. Uwe Mèffert manufactured the cube and sold it in Hong Kong in 1983.

There are 98 pieces on the exterior of the cube: 8 corners, 36 edges, and 54 centers (48 movable, 6 fixed).

Any permutation of the corners is possible, including odd permutations, giving 8! possible arrangements. Seven of the corners can be independently rotated, and the orientation of the eighth corner depends on the other seven, giving 37 (or 2,187) combinations.

There are 54 centers. Six of these (the center square of each face) are fixed in position. The rest consist of two sets of 24 centers. Within each set there are four centers of each color. Each set can be arranged in 24! different ways. Assuming that the four centers of each color in each set are indistinguishable, the number of permutations of each set is reduced to 24!/(246) arrangements, all of which are possible. The reducing factor comes about because there are 24 (4!) ways to arrange the four pieces of a given color. This is raised to the sixth power because there are six colors. The total number of permutations of all movable centers is the product of the permutations of the two sets, 24!2/(2412).