In the numerator you want to have a polynomial of a lesser degree than in the denominator, otherwise partial fractions won't work. in this exercises you have something quadratic both up and down. denominator is (p+1)(p+5) so you rewrite the numerator as
(p+1)(p+5) + something
now you divide and you get
1 + something/(p+1)(p+5)
and "something" will have lesser degree than two so you can apply the partial fractions decomposition.
