Five, Given that line $l$ is tangent to the unit circle $\odot O$ at point $P$, point $A$ is on the same side of line $l$ as $\odot O$, and the distance from $A$ to line $l$ is $h(h>2)$, two tangents are drawn from point $A$ to $\odot O$, intersecting line $l$ at points $B$ and $C$. Find the product of the lengths of segments $P B$ and $P C$.
Five, As shown in Figure 2, let the lengths of $PB$ and $PC$ be $p$ and $q$, respectively, $\angle ABP = \beta$, $\angle ACP = \gamma$, and the point where $AC$ touches $\odot O$ be $E$, with the length of $AE$ being $t$. Connecting $AO$ and $OE$, in the right triangle $\triangle AOE$, we have $\angle AOE = \frac{1}{2}(\beta + \gamma)$.
Therefore, $t = \tan \frac{1}{2}(\beta + \gamma) = \frac{p + q}{pq - 1}$. From this, we get
$$
S_{\triangle BUC} = (p + q + t) \times 1 = \frac{pq(p + q)}{pq - 1}.
$$

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

Thus, $pq = \frac{h}{h - 2}$.