5 Given a line $l$ tangent to the unit circle $S$ at point $P$, point $A$ is on the same side of $l$ as circle $S$, and the distance from $A$ to $l$ is $h(h>2)$. Two tangents are drawn from point $A$ to $S$, intersecting $l$ at points $B$ and $C$. Find the product of the lengths of segments $PB$ and $PC$. (Leng Gangsong, Si Lin)
Let the lengths of $PB$ and $PC$ be $p$ and $q$, respectively. Let $\angle ABP = \beta$ and $\angle ACP = \gamma$. Let the point where $AC$ touches $S$ be $E$, and let the center of the circle be $O$. Let the length of $AE$ be $t$. Connecting $AO$ and $OE$, we have in the right triangle $AOE$:
$$
\angle AOE = \frac{1}{2}(\beta + \gamma),
$$

Therefore,
$$
t = \tan \frac{1}{2}(\beta + \gamma) = \frac{p + q}{pq - 1}.
$$

Thus, the area of $\triangle ABC$, $S_{\triangle ABC}$, is
$$
S_{\triangle ABC} = (p + q + t) \times 1 = \frac{pq(p + q)}{pq - 1}.
$$

Since $S_{\triangle ABC} = \frac{1}{2}(p + q) \times h$,
we have
$$
\frac{1}{2} h = \frac{pq}{pq - 1}.
$$

Rearranging, we get
$$
pq = \frac{h}{h - 2}.
$$