Math is really tricky!

Algebra Level 3

A monic polynomial \(f(x)\) of degree 5 is such that \[\begin{cases} f(0)=1 \\ f(1)=2 \\ f(2)=5 \\ f(3)=10 \\ f(4)=17. \end{cases} \] What is the value of \(f(5)?\)

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