1. The problem asks to find the value of $h^{-1}(3)$ given that $h(5) = 3$. 2. Recall that $h^{-1}$ is the inverse function of $h$, which means that if $h(a) = b$, then $h^{-1}(b) = a$. 3. Since $h(5) = 3$, by the definition of inverse functions, $h^{-1}(3) = 5$. 4. Therefore, the answer is $\boxed{5}$.