(5) $\sin 6^{\circ} \sin 42^{\circ} \sin 66^{\circ} \sin 78^{\circ}=$
(5) $\frac{1}{16}$ Hint:
$$
\begin{array}{l}
\sin 6^{\circ} \cos 48^{\circ} \cos 24^{\circ} \cos 12^{\circ} \\
=\frac{\cos 6^{\circ} \sin 6^{\circ} \cos 48^{\circ} \cos 24^{\circ} \cos 12^{\circ}}{\cos 6^{\circ}} \\
=\frac{\sin 12^{\circ} \cos 12^{\circ} \cos 24^{\circ} \cos 48^{\circ}}{2 \cos 6^{\circ}} \\
=\frac{\sin 24^{\circ} \cos 24^{\circ} \cos 48^{\circ}}{4 \cos 6^{\circ}} \\
=\frac{\sin 48^{\circ} \cos 48^{\circ}}{8 \cos 6^{\circ}} \\
=\frac{\sin 96^{\circ}}{16 \cos 6^{\circ}}=\frac{1}{16} .
\end{array}
$$