Non-Elementary Integration · Medium problem

Using $\displaystyle\int_0^{\pi/2}\sin^{2a-1}x\cos^{2b-1}x\,dx=\dfrac12B(a,b)=\dfrac{\Gamma(a)\Gamma(b)}{2\Gamma(a+b)}$, evaluate $\displaystyle\int_0^{\pi/2}\sin^3x\cos^5x\,dx$.