jmc

Begin by drawing a segment from $A$ to $E$ parallel to $CB$. We have that $AE=BC=8$. Then, $DE=DC-5=20-5=15$. Now, we can apply the Pythagorean Theorem to find $AD$. $$A{D}^2=8^2+15^2=289=17^2$$ $$AD=\boxed{17}$$