5. 若 $\cos (\alpha+\beta) \cos \alpha+\sin (\alpha+\beta) \sin \alpha=-\frac{4}{5}$, 且 $450^{\circ}<\beta<540^{\circ}$, 则 $\sin \left(60^{\circ}-\beta\right)=$
由已知得 $\cos [(\alpha+\beta)-\alpha]=\cos \beta=-\frac{4}{5}$,

$\because 450^{\circ}<\beta<540^{\circ}, \therefore \sin \beta=\frac{3}{5}$,

$\therefore \sin \left(60^{\circ}-\beta\right)=\frac{\sqrt{3}}{2} \times\left(-\frac{4}{5}\right)-\frac{1}{2} \times \frac{3}{5}=-\frac{3+4 \sqrt{3}}{10}$.