Does pattern always true?

Algebra Level 4

Let p(x)p(x) be a polynomial of degree 4 with real coefficients satisfying p(0)=0p(0)=0, p(1)=12p(1)=\dfrac{1}{2}, p(2)=23p(2)=\dfrac{2}{3}, p(3)=34p(3)=\dfrac{3}{4} and p(4)=45p(4)=\dfrac{4}{5}. Evaluate the value of p(5)p(5). Enter your answer with 3 significant figures.

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