Polyominoes Challenge

Pentomino Puzzle
In 1953 a mathematician named Solomon Golomb invented the idea of polyominoes: geometric shapes made by connecting a certain number of squares with their sides matching.

Here are a few sample polyominoes:

You are going to design pentominoes. A pentomino is made out of five congruent squares. Each square must share at least one complete side of another one of the five squares. The sides may not overlap. Your challenge is to find all the possible pentomino designs. You can use graph paper or drawings to record your solutions.