A quintic equation?! Think differently

Algebra Level 2

\[ \large {\begin{cases} {x-y=7} \\ {x^2+y^2 = 85} \end{cases} } \]

Let \(x\) and \(y\) be positive real numbers that satisfy the system of equations above. What is the value of \(x^5 - y^5 \)?

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