The reason for chromium to have ${\text{[Ar]\hspace{0.17em}4s}}^{1}3{\text{d}}^{\text{5}}$ is

If two (or) more electrons have same spin can exchange each other in the degenerate orbitals. Exchange energy increases if the number of electrons with same spin is increased.

Exchange Energy  $\text{E}=\frac{\text{k}.n.(n-1)}{2}$

Here K = exchange energy constant

N = No. of electrons with the same spin