Boundary Values & Fourier Series · Hard problem

Let $f$ be the $2\pi$-periodic square wave equal to $-2$ on $(-\pi, 0)$ and $2$ on $(0, \pi)$. Find the Fourier sine coefficient $b_{5} = \dfrac{1}{\pi}\int_{-\pi}^{\pi} f(x)\sin(5x)\,dx$. Give an exact answer in terms of $\pi$.