Suppose that \(x\) and \(y\) are positive real numbers satisfying \(x^2+y^2 = 5xy\). Then \( \frac{x-y}{x+y} \) can be written as \( \sqrt{\frac{a}{b}} \), where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

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