There is already a "make your own pentominoesinstructable by Jonntx here:
I suggest making pentominoes out of alphabet blocks. They are so much more interesting because you can build with them. That and you can try to solve for the 2 x 5 x 6 shape or the 3 x 4 x 5 shape. :-)
Step 1: Gather Alphabet Blocks
Find your alphabet blocks. These are little ones I found in a hobby store. They are about 5/8" (five eighths of an inch (1.5 cm)) cubed. You will need 60 of them. Yes, sixty. You can also use the bigger ones which are about 1 1/4" (one and one quarter inches (3.2 cm)) cubed. You can find them at toy stores and online. I repeat, you will need sixty of them.
You will also need glue and rubber bands.
Step 2: Get to Know Your Pentominoes
There are twelve unique shapes in pentominoes all made out of five cubes each. Based on the shapes, they are all named after letters. Most of very obvious, that is the "L" shaped piece is called the "L." Other pieces need a bit of an imagination. The shapes/letters are
F, I, L, N, P, T, U, V, W, X, Y, Z.
The way to remember the letters is the nonsense word, "filnop" and the end of the alphabet, T through Z.
Here are the first five shapes/letters:
Step 3: The Next Seven Pieces
These are the end of the alphabet series, pieces T through Z.
Step 4: Glue - Start With the Easy Ones
For the "I" - Line up five blocks, and glue them together. Wrap a rubber band around them to hold them in place. Neatness counts. The flatter they are now the less wobbly they are later.
For the "L" - Line up four blocks, glue and wrap them with a rubber band. Add one block on one end to make the "L."
For the "Y" - Line up four blocks, glue and wrap them with a rubber band. Add one block onto the block next to the end.
There is only one "gotcha" in this. When you get to the "U" piece, make sure you make it wide enough so that another piece will fit in it. Or you can sand it down after it is all glued, but why bother. Just make sure the space is big enough.
Repeat creating each of the twelve pieces. Put them away to dry overnight or so.
Step 5: Playing With the Pentominoe Pieces
Now that you have a set of pentominoes, what do you do with them? You have twelve pieces, each made up of five blocks, or 60 blocks. Here are just some of the shapes you can make:
1 x 6 x 10 - 2339 solutions (not counting rotations and mirror images)
1 x 5 x 12 - 1010 solutions
1 x 4 x 15 - 368 solutions
1 x 3 x 20 - two solutions
2 x 5 x 6
3 x 4 x 5