Let $f, g : \mathbb{Z}/5\mathbb{Z} \rightarrow S_5$ be two non-trivial group homomorphisms. Show that there is a $\sigma \in S_5$ such that $f(x) = \sigma g(x) \sigma^{-1}$, for every $x \in \mathbb{Z}/5\mathbb{Z}$.
Let $f, g : \mathbb{Z}/5\mathbb{Z} \rightarrow S_5$ be two non-trivial group homomorphisms. Show that there is a $\sigma \in S_5$ such that $f(x) = \sigma g(x) \sigma^{-1}$, for every $x \in \mathbb{Z}/5\mathbb{Z}$.