No one knows by whom or when pentominoes were first discovered, someone had to have been first.
Perhaps it was a mathematician from the middle east or a chinese astrologer from some early dynastic period? Whatever the case they keep getting rediscovered and provide a fascinating set of challenges
for any one with enough time on their hands. The game tetris came out of a failed attempt to to program a computer to solve the 5 x 12 problem.
These pentomino pages provide a few of the myriad, although arguably finite, solutions to the puzzles that can be posed by their existence.