Infinity is lovely

Algebra Level 4

K=5+55+55+K= \large \sqrt{5 + \sqrt{5-\sqrt{5+\sqrt{5-\sqrt{5+\ldots}}}}}

If KK can be expressed in simplest form as a+bc\dfrac{a+\sqrt{b}}{c}, where a,b,ca,b,c are positive integers, find the value of a2+b2+c2a^2+b^2+c^2.

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