Checkerboard-proof

The 5 different tetrominoes, when placed on a checkerboard, allways have 9 squares in one color, and 11 squares in the other color.

Combinations of four X-pentominoes have 4/16, 7/13 of10/10 colouring.

Therefor four X pentominoes can never be arranged to make a figure made from the 5 different tetrominoes.