Inspiration

Algebra Level 4

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

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