This happens to be a long integral.

But the first set is to use integration by part,

u=x and v'=sin^5 x

Thus, u'=1

But when you find v you need to find the integral of sin^5 x which you can do by writing it as:

sin^5 x=sin^4 x sin x = (1-cos^2x)^2*sin x

Then use the substitution t=sin x.

But after you do that long integration by parts you will need to do another trigonometric integral like the one above.