Let $\displaystyle f,g :\mathbb{Z}/5\mathbb{Z} \to S_{5}$ be 2 non trivial group homomorphisms. Prove that there exists a $\displaystyle \sigma \in S_{5}$ such that $\displaystyle f(x)=\sigma g(x) \sigma^{-1}$ for every $\displaystyle x \in \mathbb{Z}/5\mathbb{Z}$