Five, natural number $n \geqslant 3$. In the plane, a line $l$ is given, on which there are $n$ distinct points $P_{1}, P_{2}, \cdots, P_{n}$ in sequence. The product of the distances from point $P_{i}$ to the other $n-1$ points is denoted as $d_{i}(i=1,2, \cdots, n)$. There is also a point $Q$ in the plane not on $l$, and the distance from point $Q$ to point $P_{i}$ is denoted as $C_{i}(i=1,2, \cdots, n)$. Find the value of the following sum:
$$
S_{n}=\sum_{i=1}^{n}(-1)^{n-i} \frac{C_{i}^{2}}{d_{i}} .
$$
Let's assume these $n$ points are on the real axis, with coordinates $P_{i}\left(x_{i}, 0\right) (i=1,2, \cdots, n), x_{1}3 \text { when. }
\end{array}\right.
$$

Substituting into (1) we get
$$
\begin{aligned}
S_{n} & =\left(a^{2}+\beta^{2}\right) T_{0}-2 \alpha T_{1}+T_{2}=T_{2} \\
& =\left(\begin{array}{l}
1, n=3 \text { when, } \\
0, n>3 \text { when. }
\end{array}\right.
\end{aligned}
$$