5. In trapezoid $A B C D$, $A D / / B C, B C=B D$, $A D=C D$, and $\angle C=80^{\circ}$. Then the degree measure of $\angle A$ is ( ).
(A) $120^{\circ}$
(B) $130^{\circ}$
(C) $140^{\circ}$
(D) $150^{\circ}$
5. D.

It is known that $\angle B D A=20^{\circ}$.
Construct a regular $\triangle C D O$ inward with $C D$ as a side, and connect $O B$.
Then $\triangle A B D \cong \triangle O B D \cong \triangle O B C$.
Thus, $\angle A=\angle D O B=150^{\circ}$.