5. In a convex quadrilateral $A B C D$, $A C$ bisects $\angle B A D$, and $C B = C D$. Then the relationship between $\angle B$ and $\angle D$ is ( ).
(A) equal
(B) unequal
(C) equal or supplementary
(D) complementary or supplementary
$\begin{array}{l}\text { 5. (C). } \\ \text { As shown in figure } 4, \text { when } A B \\ =A D, \triangle A B C \\ \cong \triangle A D C, \\ \text { when } A B \neq A B, \\ \text { construct } \triangle A B^{\prime} C \cong \\ \triangle A I C. M, \\ \angle B = \angle D \\ \text { or } \angle B \text { and } \angle D \text { are } \\ \text { supplementary. } \\\end{array}$