\(f\) is not injective, since \(f(2) = f(5)\text{;}\) two different inputs have the same output.
\(f\) is surjective, since every element of the codomain is an element of the range.
\(f=\begin{pmatrix}1 \amp 2 \amp 3 \amp 4 \amp 5 \\ 3 \amp 2 \amp 4 \amp 1 \amp 2\end{pmatrix}\text{.}\)