$$\lim_{n \to \infty} \frac{5 ^n}{\left(5-\sqrt{3}+2\sin x^\circ \right)^{n+2}} = \frac{1}{y}$$

Calculus Level 2

For a certain positive real number $$0 \leq x \leq 90$$, there is a real number $$y$$ such that

$\lim_{n \to \infty} \frac{5 ^n}{\left(5-\sqrt{3}+2\sin x^\circ \right)^{n+2}} = \frac{1}{y}.$

What is the value of $$x + y$$?

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