5. Given $\boldsymbol{a}=(\cos \alpha, \sin \alpha), \boldsymbol{b}=(\cos \beta, \sin \beta)$, $|a-b|=\frac{2 \sqrt{5}}{5}$. If $0<\alpha<\frac{\pi}{2},-\frac{\pi}{2}<\beta<0$, and $\sin \beta=-\frac{5}{13}$, then $\sin \alpha=(\quad)$.
(A) $\frac{31}{65}$
(B) $\frac{32}{65}$
(C) $\frac{33}{65}$
(D) $\frac{34}{65}$