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

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