5. Let $Z$, $W$, and $\lambda$ be complex numbers, $|\lambda| \neq 1$. For the equation $\bar{Z} - \lambda Z = W$ with respect to $Z$, the following four conclusions are given:
I. $Z = \frac{\bar{\lambda} W + \bar{W}}{1 - |\lambda|^2}$ 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 III are correct
C. Only I and IV are correct
D. None of A, B, C are correct
Solve
$\bar{Z}-\lambda Z=W \Rightarrow Z-\bar{\lambda} \cdot \bar{Z}=\bar{W} \Rightarrow\left\{\begin{array}{l}\bar{\lambda} \cdot \bar{Z}-\bar{\lambda} \cdot \lambda Z=\bar{\lambda} \cdot W, \\ Z-\bar{\lambda} \cdot \bar{Z}=\bar{W}\end{array}\right.$ $\Rightarrow Z(1-\bar{\lambda} \cdot \lambda)=\bar{W}+\bar{\lambda} \cdot W \Rightarrow Z=\frac{\bar{\lambda} \cdot W+\bar{W}}{1-|\lambda|^{2}}$, which means the equation has only one solution. Therefore, only I and II are correct, so the answer is $A$.