Eithan Samara wrote this Java applet after he searched the whole web for a solver to the 3D pentominoes puzzle problem and didn't find any. He used his own 3D graphics libraries in order to make the 3D engine work faster and make the applet as lighter as it could get (the Jar file size is 31KB).

The solver can solve both by box size (container) and by piece, which means creating a copy of a single pentomino with double magnification and triple height. The 'Special' option on the 'By Box' menu will solve for a unique box with a size of 3 x 5 x 5 and a hole in the middle.
The 'Lined' checkbox will show all pentominoes formed from their basic 1 x 1 x 1 cubes. Checking the 'Animate' checkbox will show the way the backtracking algorithm tries to solve the problem, but it would also make the solving process much slower.
The number of steps shown on the lower-left corner of the applet counts the number of pentominoes pieces the solver tried to place so far.

Below there is the data for the number of steps the solver needs in order to reach the first solution in each solving option:

Author: Eithan Samara
Source: http://www.panda.co.il/eithan/pento/Pentominoes3D.html, last updated 1 July 2005