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.