Terrible Integrals!

Calculus Level 4

\[ \large \displaystyle \int _{ 0 }^{ \frac { \pi }{ 2 } }{ \sin ^{ 5 }{ (x) } \cos ^{ 3 }{ (x) } \ dx } = \ ?\]

If the closed form of the integral above is in the form of \( \dfrac{a}{b}\), where \(a\) and \(b\) are natural numbers and \( \gcd(a,b)=1\), find \(a+b\).

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