(5) Given the function $f(x)$ satisfies the condition $f(a x-1)=\lg \frac{x+2}{x-3}(a \neq 0)$.
(1) Find the expression for $f(x)$;
(2) Find the domain of $f(x)$;
(3) Does there exist a real number $a$ such that $f(x)$ is an odd function or an even function? If so, find the value of $a$; otherwise, explain the reason.
$$
\begin{array}{l}
\text { (1) } f(x)=\lg \frac{x+(2 a+1)}{x+(-3 a+1)} \quad \text { (2) } D=\{x \mid[x+(2 a+1)][x+ \\
(-3 a+1)]>0, x \in \mathbf{R}\}=\left\{\begin{array}{ll}
(-\infty,-2 a-1) \cup(3 a-1,+\infty), a>0, \\
(-\infty, 3 a-1) \cup(-2 a-1,+\infty), a<0
\end{array}\right.
\end{array}
$$
(3) When $a=0.2$, $f(x)$ is an odd function
$$