5. $\frac{\sin 7^{\circ}+\sin 8^{\circ} \cos 15^{\circ}}{\cos 7^{\circ}-\sin 8^{\circ} \sin 15^{\circ}}=$
$\begin{array}{l}\text { 5. } 2-\sqrt{3} \text {. } \\ \sin 7^{\circ}=\sin \left(15^{\circ}-8^{\circ}\right)=\sin 15^{\circ} \cos 8^{\circ}-\cos 15^{\circ} \sin 8^{\circ} \text {, then } \sin 7^{\circ}+\sin 8^{\circ} \cos 15^{\circ}=\sin 15^{\circ} \cos 8^{\circ} \text {. } \\ \text { Similarly, } \cos 7^{\circ}-\sin 8^{\circ} \sin 15^{\circ}=\cos 8^{\circ} \cos 15^{\circ} \text {, so } \\ \frac{\sin 7^{\circ}+\sin 8^{\circ} \cos 15^{\circ}}{\cos 7^{\circ}-\sin 8^{\circ} \sin 15^{\circ}}=\frac{\sin 15^{\circ} \cos 8^{\circ}}{\cos 15^{\circ} \cos 8^{\circ}}=\tan 15^{\circ}=\tan \left(45^{\circ}-30^{\circ}\right)=2-\sqrt{3} \text {. }\end{array}$