5. Given: As shown in Figure 2, the radius of $\odot$ O is $5 \mathrm{~cm}$, P is a point outside $\odot O$, $P O=17 \mathrm{~cm}$, $P C D$ intersects $\odot 0$ at $C$, $\mathrm{PC}: \mathrm{CD}=2: 1$. Find the length of $\mathrm{PD}$.
5. Solution As shown in Figure 5, extend

PO to intersect circle O at F.
$$
\begin{array}{l}
\because O E=5 \mathrm{~cm}, \\
O P=17 \mathrm{~cm}, \\
\therefore P E=12 \mathrm{~cm}, \\
P F=22 \mathrm{~cm} .
\end{array}
$$
$\because \mathrm{PC}: \mathrm{CD}=2: 1$, let $\mathrm{CD}$ be $\mathrm{xcm}$, then $\mathrm{PC}$ is $2 \mathrm{xcm}$, and $\mathrm{PD}$ is $3 \mathrm{xcm}$.
$$
\text { By } \mathrm{PC} \cdot \mathrm{PD}=\mathrm{PE} \cdot \mathrm{PF} \text {, }
$$

we have $2 \mathrm{x} \cdot 3 \mathrm{x}=12 \times 22$,
$$
\begin{aligned}
6 x^{2} & =12 \times 22 \\
x^{2} & =44, \\
x & =2 \sqrt{11}, \quad 3 x=6 \sqrt{11} .
\end{aligned}
$$

Answer: PD is $6 \sqrt{11} \mathrm{~cm}$.