Inspiration

Algebra Level 4

mnf(n)0112216321644096\begin{array}{c}m n & f(n) \\ 0 & 1 \\ 1 & 2 \\ 2 & 16 \\ 3 & 216 \\ 4 & 4096\end{array}

Given that f(n)f(n) is a 4th4^\text{th} degree polynomial satisfying the relationship as shown above, find f(5)f(5).

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