Let C = [A|b] where [A|b] is the augmented matrix of order 3X5.
Here, maximum possible $\rho$(C) = min(3, 5) $\implies$ $\rho$(C) = 3
Now, in case of inconsistency $\rho$(A) $\lt$ $\rho$(C) $\implies$ $\rho$(A) $\lt$ 3
So, the maximum possible rank of A is 2.