5. In the Cartesian coordinate system, let point $A(-8,3)$, $B(-4,5)$, and moving points $C(0, n)$, $D(m, 0)$. When the perimeter of quadrilateral $A B C D$ is minimized, the ratio $\frac{m}{n}$ is ( ).
(A) $-\frac{2}{3}$
(B) -2
(C) $-\frac{3}{2}$
(D) -3
As shown in Figure 13, let the symmetric point of point $A$ with respect to the $x$-axis be $A^{\prime}$, and the symmetric point of point $B$ with respect to the $y$-axis be $B^{\prime}$. Then $A(-8,-3)$, $B^{\prime}(4,5)$.

Therefore, when points $C$ and $D$ are both on the line $A^{\prime} B^{\prime}$, the perimeter of quadrilateral $A B C D$ is minimized.
Thus, $m=-\frac{7}{2}, n=\frac{7}{3} \Rightarrow \frac{m}{n}=-\frac{3}{2}$.