5. Let $Z, W, \lambda$ be complex numbers, $|\lambda| \neq 1$, and the equation $\bar{Z}-\lambda Z=W$ has the following four conclusions about $Z$:
I. $Z=\frac{\bar{\lambda} W+\bar{W}}{1-|N|^{2}}$ is a solution to this equation;
II. This equation has only one solution;
III. This equation has two solutions;
IV. This equation has infinitely many solutions. Then
(A) Only I and II are correct
(B) Only I and IV are correct
(C) Only I and III are correct
(D) None of (A), (B), (C) are correct
5.【Analysis and Solution】From the four conclusions given in the problem, we know that this question requires making a choice based on the solution of the equation. Therefore, consider taking the conjugate of both sides of the equation $\bar{Z}-\lambda Z=W$, resulting in $Z-\overline{\lambda Z}=\bar{W}$,
multiplying both sides by $\lambda$, we get $\lambda Z-|\lambda|^{2} \bar{Z}=\lambda \bar{W}$.
Adding this to the original equation, we get $\bar{Z}\left(1-|\lambda|^{2}\right)=\lambda \bar{W}+W$,
taking the conjugate of both sides again, we get $Z\left(1-|\lambda|^{2}\right)=\bar{\lambda} W+\bar{W}$.
$$
\because|\lambda|^{2} \neq 1, \quad \therefore Z=\frac{\bar{\lambda} W+\bar{W}}{1-|\lambda|^{2}} .
$$