${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}si{n}^{5}xcosxdxis$:

$A\frac{1}{12}si{n}^{6}xco{s}^{2}x+C$

$B\frac{1}{6}si{n}^{6}xcosx+C$

$C-si{n}^{6}x+5si{n}^{4}xco{s}^{2}x+C$

$D\frac{1}{6}si{n}^{6}x+C$

$E\frac{1}{6}si{n}^{7}x+C$