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

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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