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

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

**Notations**:

\( H_n\) denotes the \(n^\text{th} \) harmonic number, \( H_n = 1 + \dfrac12 + \dfrac13 + \cdots + \dfrac1n\).

\(\zeta(\cdot) \) denotes the Riemann zeta function.

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