A quintic equation?! Think differently

Algebra Level 2

{x−y=7x2+y2=85 \large {\begin{cases} {x-y=7} \\ {x^2+y^2 = 85} \end{cases} }

Let xx and yy be positive real numbers that satisfy the system of equations above. What is the value of x5−y5x^5 - y^5 ?

Denton Young by Denton Young
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