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mnf(n)0112216321644096\begin{array}{c}m n & f(n) \\ 0 & 1 \\ 1 & 2 \\ 2 & 16 \\ 3 & 216 \\ 4 & 4096\end{array}mn01234f(n)12162164096
Given that f(n)f(n)f(n) is a 4th4^\text{th}4th degree polynomial satisfying the relationship as shown above, find f(5)f(5)f(5).
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