5. Given four points in the Cartesian coordinate system $A(-2,4)$, $B(-2,0)$, $C(2,-3)$, and $D(2,0)$. Let $P$ be a point on the $x$-axis, and after connecting $P A$ and $P C$, the two triangles formed with $A B$, $C D$, and the $x$-axis (i.e., $\triangle P A B$ and $\triangle P C D$) are similar. Then the number of all points $P$ that satisfy the above conditions is ( ).
(A) 2
(B) 3
(C) 4
(D) 5
5.C.
(1) $A B$ and $C D$ are corresponding sides.
(i) $P$ is the intersection point of $A C$ and the $x$-axis. The equation of $A C$ is $y=-\frac{7}{4} x+\frac{1}{2}$, giving $x=\frac{2}{7}, y=0$.
(ii) Take the point $C$'s reflection about the $x$-axis, $C^{\prime}(2,3)$, $P$ is the intersection point of $A C^{\prime}$ and the $x$-axis. The equation of $A C^{\prime}$ is $y=-\frac{1}{4} x+\frac{7}{2}$, giving $x=14, y=0$.
(2) $A B$ and $C D$ are not corresponding sides, i.e., $\frac{P B}{A B}=\frac{C D}{P D}$.
Let point $P(x, 0)$. Then
$$
\begin{array}{l}
\frac{|x+2|}{4}=\frac{3}{|x-2|} \\
\Rightarrow\left|x^{2}-4\right|=12 \Rightarrow x= \pm 4 .
\end{array}
$$

Therefore, there are 4 points $P$ that meet the conditions, which are
$$
\left(\frac{2}{7}, 0\right),(14,0),(4,0),(-4,0) \text {. }
$$