Given a function $f : X \rightarrow X $  

It is known that $f^5 = I$ where $I(x) = x$ (The identity function)  

I need to prove that $f$ is bijective (Injective and Surjective) 

$f^n = f \circ f \circ f ...\circ f$ 

I've tried many ways such as finding out whether or not $x\_1, x\_2 \in X$ exist such that $f(x\_1) = f(x\_2)$ but it did not help as the function was composed with itself (5 times) and I got stuck...