Have You Heard Of Euler's Sum?

Calculus Level 5

\[ \large \sum_{n=1}^\infty \dfrac{H_n}{n^5} = \dfrac{\pi^A}{B} - \dfrac{(\zeta (D))^C}{E} \]

If the equation above holds true for positive integers \(A,B,C,D\) and \(E\), find \(A+B+C+D+E\).

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