Diagonally Magnetized Pentominoes

Here are the 34 pieces packed in two 5x17 rectangles.

Since 5*5+3*3=34 you might think it's easy to get a 5-fold plus a 3-fold replica of each pentomino. But you can only do it for the I, X and Z pentomino in all orientations. If the axis of magnetization is perpendicular to the symmetry axis of the right angle in the W, V, L and N pentomino a solution is possible, too. In any other case we have a constraint adding the sum of x and y coordinates mod 5 for all covered squares.

An equivalent set with shingle like forms.