5. In the plane, let the graph of the function $f(x)$ be symmetric to the graph of $y=$ $-2 x^{2}$ with respect to the line $y=2 x+3$, then the analytical expression of $f(x)$ is ().
(A) $3 y+4 x+6=-\frac{2}{5}(4 y-3 x-12)^{2}$
(B) $3 y+4 x+6=-10(4 y-3 x-12)^{2}$
(C) $3 y+4 x=-\frac{2}{5}(4 y-3 x)^{2}$
(D) $3 y+4 x-6=-\frac{2}{5}(4 y-3 x+12)^{2}$
5. (A).

Take a point $(x, y)$ on the graph of $f(x)$, and there is a corresponding point $\left(x^{*}, y^{*}\right)$ on $y=$ $-2 x^{2}$, such that these two points are symmetric with respect to the line $y=2 x+3$. Therefore, we have
$$
\begin{array}{l}
\frac{1}{2}\left(y+y^{*}\right)=x+x^{*}+3, \\
y^{*}-y=-\frac{1}{2}\left(x^{*}-x\right),
\end{array}
$$

Thus, $x^{*}=\frac{1}{5}(4 y-3 x-12)$,
$$
y^{*}=\frac{1}{5}(3 y+4 x+6) \text {. }
$$
The point $\left(x^{*}, y^{*}\right)$ should satisfy $y^{*}=-2 x^{* 2}$.