My question is how to find all conjugacy classes of order 5 of the rotational symmetry of the dodecahedron. I know that I could find them by considering conjugacy classes of order 5 in A5, but I would like to find them by considering the dodecahedron.
I also know that the elements of order 5 are rotations through the middle of a side of the dodecahedron. My problem is I can't visualize which rotations I have to use to prove there are two conjugacy classes of elements of order 5.