Hitting Time Between Leaves on the Star Graph S₅

The star graph $S_5$ has a central hub vertex $c$ connected to $4$ leaf vertices $\{\ell_1, \ell_2, \ell_3, \ell_4\}$. A simple random walk at each step moves to a uniformly random neighbor: from the hub, it goes to each leaf with probability $\tfrac{1}{4}$; from any leaf, it goes to $c$ with probability $1$. Starting at leaf $\ell_1$, what is the expected number of steps to reach leaf $\ell_2$ for the first time?