Guess the Polynomial

Algebra Level 4

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

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

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