5. $A\left(x_{1}, y_{1}\right), B\left(x_{2}, y_{2}\right), C\left(x_{3}, y_{3}\right), D\left(x_{4}\right.$, $\left.y_{4}\right)$ are four points on the parabola $y=a x^{2}+b x+c(a \neq 0)$, and satisfy $x_{1}+x_{4}=x_{2}+x_{3}$. Then ( ).
(A) $A D / / B C$
(B) $A D \perp B C$
(C) $A D{ }_{-j} B C$ intersect but are not perpendicular
(D) Cannot be determined, depends on the specific values of the parameters


5. (A).

The parabola has 4 points with distinct x-coordinates.
$$
\begin{aligned}
\because k_{A D} & =\frac{y_{4}-y_{1}}{x_{4}-x_{1}}=a\left(x_{4}+x_{1}\right)+b \\
& =a\left(x_{3}+x_{2}\right)+b=\frac{a\left(x_{3}^{2}-x_{2}^{2}\right)+b\left(x_{3}-x_{2}\right)}{x_{3}-x_{2}} \\
& =\frac{\left(a x_{3}^{2}+b x_{3}+c\right)-\left(a x_{2}^{2}-b x_{2}+c\right)}{x_{3}-x_{2}} \\
& =\frac{y_{3}-y_{2}}{x_{3}-x_{2}}=k_{B C}, \\
\therefore A D & / / B C .
\end{aligned}
$$