Math is really tricky!

Algebra Level 3

A monic polynomial f(x)f(x) of degree 5 is such that {f(0)=1f(1)=2f(2)=5f(3)=10f(4)=17.\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)?f(5)?

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