the idea comes from ancient philosophy, when philosophers could make claims like "everything is made of fire" or "everything is made of water" or "everything is made of triangles" and argue it reasonably. the platonic solids, also, are five in number, where the fifth is a dodecahedron. i think it was plato, among others, who also believed in a fifth element, aether, but i cant remember the details.

how one would demonstrate any of these relationships mathematically is beyond me.