I'm going through some practice prelim exams, and one of the questions asks to compute $ \int_{|z|=2}\frac{z^4}{z^5-z-1}dz. $
The integrand is not quite in the form $f'/f$ to count zeroes and poles inside the circle. I wanted to compute resides, but finding the poles at which to calculate them seems more difficult than usual. What is the more doable approach?