Should the equation be p^2+5p+5=0? To complete the square: p^2+5p+(5/2)^2=(5/2)^2-5, and (p+5/2)^2=(5/2)^2-5. So p+5/2=+/-sqrt(25-20)/2=+/-sqrt(5)/2 and p=(-5+/-sqrt(5))/2, which is option b without the 3.
If the question is p^2+5p-5=0 or p^2+5p=5, then (p+5/2)^2=(5/2)^2+5 and p+5/2=+/-sqrt(25+20)/2=+/-sqrt(45)/2=+/-sqrt(9*5)/2=+/-3sqrt(5)/2. Therefore p=(-5+/-3sqrt(5))/2, option b.