5. As shown in Figure 11, the base of the pyramid $S-ABCD$ is a rectangle $ABCD$ with center $O$, where $AB=4$, $AD=12$, $SA=3$, $SB=5$, and $SO=7$. A section of the pyramid is made through the vertex $S$, the center $O$ of the base, and a point $N$ on the edge $BC$. What is the value of $BN$ when the area of the resulting section $\triangle SMN$ is minimized? What is this minimum value?
(Tip: From the conditions, it is easy to know that $S A \perp$ plane $A B C D$. Also, $O M = O N$, so $S_{\triangle \operatorname{seN}} = 2 S_{\triangle \text{ Swo }}$. It is easy to know that when the distance from point $M$ to $S O$ is the distance between the skew lines $A B$ and $S O$, $S_{\triangle \operatorname{sen} 0}$ is minimized. At this time, $S_{\triangle \text{ sem }} = \frac{42 \sqrt{13}}{13}, B N = 7 \frac{11}{13}.$)