The Professor's Cube is a 5x5x5 verion of the original Rubik's Cube. The first version of this puzzle was invented in 1986 by Udo Krell, who took a 3x3x3 cube and expanded it.
As with the Rubik's Revenge (4x4x4), the most common algorithm for solving this 5x5x5 cube is called the "reduction" method. Focusing on solving the 3x3 center pieces and 3x1 edge pieces first - thus "reducing" the problem to a 3x3x3 puzzle, which can be solved using a regular Rubik's cube solving algorithm. This puzzle has only one parity case.
This puzzle has many moving parts thus allowing a huge number of possible permutations. The number of possible permutations of the 5x5x5 Cube is just under 2.83x1074. The Current world record for solving it is 41.57 seconds, and it was set by Australian Feliks Zemdegs at Melbourne Cube Day 2016.