Find the Integral $\int \cos ^{5} x \sin ^{2} x d x$

Multiple Choice

Find the integral. $\int \cos ^{5} x \sin ^{2} x d x$

A) $\frac{1}{5} \sin ^{5} x-\frac{2}{3} \sin ^{3} x+\sin ^{3} x+C$
B) $\frac{1}{7} \sin ^{7} x-\frac{2}{5} \sin ^{5} x+\frac{1}{3} \sin ^{3} x+C$
C) $\frac{1}{5} \sin ^{5} x+\frac{2}{3} \sin ^{3} x-\sin ^{3} x+C$
D) $\frac{1}{7} \sin ^{7} x+\frac{2}{5} \sin ^{3} x-\frac{1}{3} \sin ^{3} x+C$