The Set of Tetrominoes

Here is the complete set of tetrominoes. Each shape consists of 4 squares, connected along their edges (not just at the corners):

Is it 5 or 7 pieces?

It depends if we can flip the shapes:

• The 7 "One-Sided" Shapes: This is the Tetris version. Since we can't flip pieces over in the game, mirror images (like J and L) are counted as different
• The 5 "Free" Shapes: This is the math version. If we can pick the pieces up and flip them over, J and L become the same shape, likewise S and Z