5. Let $a, b$ be two positive numbers, and $a>b$. Points $P, Q$ are on the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. If the line connecting point $A(-a, 0)$ and $Q$ is parallel to the line $O P$, and intersects the $y$-axis at point $R$, where $O$ is the origin, then $\frac{|A Q| \cdot|A R|}{|O P|^{2}}=$ $\qquad$ .
5.2.

Let $A Q:\left\{\begin{array}{l}x=-a+t \cos \theta \\ y=t \sin \theta\end{array}\right.$ ( $t$ is a parameter ).
Substitute (1) into $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, we get
$t=\frac{2 a b^{2} \cos \theta}{b^{2} \cos ^{2} \theta + a^{2} \sin ^{2} \theta}$.
Then $|A Q|=\frac{2 a b^{2}|\cos \theta|}{b^{2} \cos ^{2} \theta+a^{2} \sin ^{2} \theta}$.
In (1), let $x=0$, we get $t=\frac{a}{\cos \theta}$.
Then $|A R|=\frac{a}{|\cos \theta|}$.
Also, let $O P:\left\{\begin{array}{l}x=t^{\prime} \cos \theta \\ y=t^{\prime} \sin \theta\end{array}\right.$ ( $t^{\prime}$ is a parameter).
Substitute (2) into $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, we get
$t^{\prime 2}=\frac{a^{2} b^{2}}{b^{2} \cos ^{2} \theta+a^{2} \sin ^{2} \theta}$.
Then $|O P|^{2}=\frac{a^{2} b^{2}}{b^{2} \cos ^{2} \theta+a^{2} \sin ^{2} \theta}$.
Therefore, $\frac{|A Q| \cdot|A R|}{|O P|^{2}}=\ldots=2$.