Guess the Polynomial

Algebra Level 4

f(1)=1f(2)=4f(3)=9f(4)=16\begin{matrix} f\left( 1 \right) & = & 1 \\ f\left( 2 \right) & = & 4 \\ f\left( 3 \right) & = & 9 \\ f\left( 4 \right) & = & 16 \end{matrix}

I am thinking of some polynomial f(x)f\left(x\right) satisfying the equations above. What is f(5)f\left(5\right)?

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