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$\begin{array}{c}m n & f(n) \\ 0 & 1 \\ 1 & 2 \\ 2 & 16 \\ 3 & 216 \\ 4 & 4096\end{array}$

Given that $f(n)$ is a $4^\text{th}$ degree polynomial satisfying the relationship as shown above, find $f(5)$.

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