5. (6 points) In the figure, $A B=A D, \angle D B C=21^{\circ}, \angle A C B=39^{\circ}$, then $\angle A B C=$ $\qquad$ degrees.
【Analysis】If you want to find the degree of $\angle A B C$, you need to find the degree of $\angle A B D$. According to $A B=A D$, the base angles are equal. Then, you can solve it using the exterior angle.

【Solution】Solution: According to the problem, we have:
$$
\angle D B C=21^{\circ}, \angle A C B=39^{\circ}
$$

According to the property that the exterior angle equals the sum of the non-adjacent interior angles, $\angle A D B=\angle C+\angle D B C=21^{\circ}+39^{\circ}=60^{\circ}$.
$$
\begin{array}{l}
\because A B=A D . \quad \therefore \angle A D B=\angle A B D=60^{\circ} . \\
\angle A B C=\angle A B D+\angle D B C=60^{\circ}+21^{\circ}=81^{\circ} .
\end{array}
$$

Therefore, the answer is: 81