Non-Elementary Integration · Easy problem

Queen's rule says $\displaystyle\int_0^{2a} f(x)\,dx=\int_0^{a}\bigl(f(x)+f(2a-x)\bigr)\,dx$. Given $\displaystyle\int_0^{\pi/2}\sin^5 x\,dx=\dfrac{8}{15}$, evaluate $\displaystyle\int_0^{\pi}\sin^5 x\,dx$.