5. The size relationship of $\log _{\sin 1} \cos 1, \log _{\sin 1} \tan 1, \log _{\cos 1} \sin 1, \log _{\cos 1} \tan 1$ is
(A) $\log _{\text {sin } 1} \cos 1<\log _{\text {cos } 1} \sin 1<\log _{\text {sin } 1} \tan 1<\log _{\text {cos } 1} \tan 1$
(B) $\log _{\text {cos } 1} \sin 1<\log _{\text {cos } 1} \tan 1<\log _{\sin 1} \cos 1<\log _{\sin 1} \tan 1$
(C) $\log _{\text {sin } 1} \tan 1<\log _{\text {cos } 1} \tan 1<\log _{\text {cos } 1} \sin 1<\log _{\sin 1} \cos 1$
(D) $\log _{\text {cos1 }} \tan 1<\log _{\sin 1} \tan 1<\log _{\sin 1} \cos 1<\log _{\text {cos } 1} \sin 1$
(C)
5. 【Analysis and Solution】From $\frac{\pi}{4}<1<\frac{\pi}{2}$, we have $0<\cos 1<\sin 1<1$, and thus $\log _{\cos 1} \sin 1>0$. Therefore, we can exclude (A) and (B), leaving only (C) and (D). Furthermore, by $\log _{\cos 1}^{\sin 1}<\log _{\cos 1}^{\cos 1}=\log _{\cos 1}^{\sin 1}<\log _{\sin 1}^{\cos 1}$, we know that (C) should be selected.