Linear Equation and Inequality

Algebra Level 5

$\begin{eqnarray} \sqrt{55} < && \sqrt{(a+5)^2 + (b+4)^2 + (c+3)^2 + (d+2)^2 +(e+1)^2} \\ &-& \sqrt{a^2 + b^2 + c^2 + d^2 + e^2} \end{eqnarray}$

Suppose that there exist real numbers $$a,b,c,d$$ and $$e$$ such that $$a+2b+3c+4d+5e=0$$ and fulfill inequality above, find the value of $$5a+4b+3c+2d+e$$.

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