Eulerian and Hamiltonian Graphs · Superchallenge problem

The Möbius ladder $M_5$ has $10$ vertices arranged on a $10$-cycle $0,1,\ldots,9$ where $i$ connects to $(i+1) \bmod 10$, plus five rungs $i$ to $i+5$ for $i=0,\ldots,4$ (every vertex has degree $3$). Counting two Hamiltonian cycles as the same when they use the same set of edges, how many distinct Hamiltonian cycles does $M_5$ have?