5. Let quadrilateral $ABCD$ be a cyclic quadrilateral, and now four relations are given.
(1) $\sin A=\sin C$;
(2) $\sin A+\sin C=0$;
(3) $\cos B+\cos D=0$;
(4) $\cos B=\cos D$.
The number of relations that always hold is ).
(A) 1
(B) 2
(C) 3
(D) 4
5. Solution Since $A B C D$ is inscribed in a circle, then $\angle A+\angle C=180^{\circ}, \angle B+\angle D=180^{\circ}$.
Thus, $\sin A=\sin C, \cos B=-\cos D$.
That is, equations (1) and (3) hold.
Wash B.