Given mean $np= 5$
Standard deviation $\sqrt {npq} =2$
$npq= 4$
$\large\frac{npq}{np}= \frac{4}{5} $
$q= \large\frac{4}{5}$
$p=1-q=1-\large\frac{4}{5}=\large\frac{1}{5}$
$np=5=n \times \large\frac{1}{5} $$=5$
$n=25$
$(n,p)$ is $(25,\large\frac{1}{5})$
Hence 4 is the correct answer.