Solution:

Assume $\sin x=t$
Therefore $\mathrm{d}(\sin \mathrm{x})=\mathrm{dt}=\cos \mathrm{x} \mathrm{dx}$
Putting $t=\sin x$ and $d t=\cos x d x$ in given equation, we get
$\int \sin ^{5} x \cos x d x=\int t^{5} d t$
On integrating we obtain
$=\frac{t^{6}}{6}+c$
Substituting the value of $t$, we get
$=\frac{\sin ^{6} \mathrm{x}}{6}+\mathrm{c}$