Infinity is lovely

Algebra Level 5

\[K= \large \sqrt{5 + \sqrt{5-\sqrt{5+\sqrt{5-\sqrt{5+\ldots}}}}} \]

If \(K\) can be expressed in simplest form as \(\dfrac{a+\sqrt{b}}{c}\), where \(a,b,c\) are positive integers, find the value of \(a^2+b^2+c^2\).

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