5. In a convex quadrilateral $A B C D$, $A B+A C+C D=16$. When the diagonals $A C$ and $B D$ are what values, will the area of quadrilateral $A B C D$ be maximized? What is the maximum area?
(Hint: Let $A B=x, A C=y$, then $C D=16-x-y$. And
$$
\begin{array}{l} 
S_{\text {quadrilateral } A B C D}=S_{\triangle A B C}+S_{\triangle C D} \\
\leqslant \frac{1}{2} x y+\frac{1}{2} y(16-x-y) \\
=-\frac{1}{2}(y-8)^{2}+32 .
\end{array}
$$

Therefore, when $\angle B A C=\angle A C D=90^{\circ}, A C=8, B D=8 \sqrt{2}$, the maximum area of quadrilateral $A B C D$ is 32. )