Manipulative limit

Calculus Level 4

\[ \large \displaystyle\lim_{x\to0} \left( \dfrac{e^{x^2}-\sqrt{\cos{(5x)}}}{x\sin{(x)}}\right) \]

If the limit above is equal to \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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