5. Let $A, B$ be two moving points on the ellipse $x^{2}+3 y^{2}=1$, and $O A \perp O B(O$ is the origin), then the product of the maximum and minimum values of $|A B|$ is $\qquad$ .
Given $A\left(r_{1} \cos \alpha, r_{1} \sin \alpha\right), B\left(-r_{2} \sin \alpha\right.$, $\left.r_{2} \cos \alpha\right)$, substituting into the ellipse equation yields
$$
\left\{\begin{array}{l}
r_{1}^{2} \cos ^{2} \alpha+3 r_{1}^{2} \sin ^{2} \alpha=1, \\
r_{2}^{2} \sin ^{2} \alpha+3 r_{2}^{2} \cos ^{2} \alpha=1
\end{array}\right.
$$
$\Rightarrow \frac{1}{r_{1}^{2}}+\frac{1}{r_{2}^{2}}=4$. Thus, $|A B|^{2}=r_{1}^{2}+r_{2}^{2}=\frac{1}{4}\left(r_{1}^{2}+r_{2}^{2}\right)\left(\frac{1}{r_{1}^{2}}+\frac{1}{r_{2}^{2}}\right) \geqslant 1$,
with equality when $r_{1}^{2}=r_{2}^{2}=\frac{1}{2}$; when $r_{1}^{2}=1, r_{2}^{2}=\frac{1}{3}$, $|A B|_{\max }=\frac{2 \sqrt{3}}{3}$.
Therefore, the product of the maximum and minimum values of $|A B|$ is $\frac{2 \sqrt{3}}{3}$.