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$K= \large \sqrt{5 + \sqrt{5-\sqrt{5+\sqrt{5-\sqrt{5+\ldots}}}}}$

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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