Eulerian and Hamiltonian Graphs · Easy problem

The wheel graph $W_5$ has a hub $H$ joined to every vertex of a $5$-cycle rim $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}1$, plus the $5$ rim edges. Any Hamiltonian cycle of $W_5$ must visit $H$ exactly once. What is the minimum possible number of spoke edges (hub-to-rim edges) that such a Hamiltonian cycle can use?