Manipulative limit

Calculus Level 3

limx0(ex2cos(5x)xsin(x)) \large \displaystyle\lim_{x\to0} \left( \dfrac{e^{x^2}-\sqrt{\cos{(5x)}}}{x\sin{(x)}}\right)

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

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