5. Let $A$ and $B$ be moving points on the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$, and $\overrightarrow{O A} \cdot \overrightarrow{O B}=0$, where $O$ is the origin. Then the distance from $O$ to the line $A B$ is $\qquad$.
5. $\frac{a b}{\sqrt{a^{2}+b^{2}}}$.

Let $A\left(x_{1}, y_{1}\right) 、 B\left(-k y_{1}, k x_{1}\right)$, and the distance from point $O$ to $A B$ be $d$. Then
$$
|O A|^{2}=x_{1}^{2}+y_{1}^{2},|O B|^{2}=k^{2}|O A|^{2} .
$$

From $\frac{x_{1}^{2}}{a^{2}}+\frac{y_{1}^{2}}{b^{2}}=1, \frac{y_{1}^{2}}{a^{2}}+\frac{x_{1}^{2}}{b^{2}}=\frac{1}{k^{2}}$, adding them yields
$$
\begin{array}{l}
\left(\frac{1}{a^{2}}+\frac{1}{b^{2}}\right)|O A|^{2}=\frac{k^{2}+1}{k^{2}} \\
\Rightarrow|O A|^{2}=\frac{a^{2} b^{2}}{a^{2}+b^{2}} \cdot \frac{k^{2}+1}{k^{2}} .
\end{array}
$$

Thus, $d^{2}=\frac{|O A|^{2}|O B|^{2}}{|A B|^{2}}=\frac{|O A|^{2}|O B|^{2}}{|O A|^{2}+|O B|^{2}}$
$$
=\frac{k^{2}|O A|^{2}}{1+k^{2}}=\frac{a^{2} b^{2}}{a^{2}+b^{2}} \text {. }
$$

Therefore, $d=\frac{a b}{\sqrt{a^{2}+b^{2}}}$.