w^3 + 5w^2 - w = 5

Are you looking for the roots of that equation? There are three of them. One of them is w=1. You can see that by inspection.

For the other roots, divide
w^3 + 5w^2 -w -5 by (w-1) and solve the resulting quadratic. You end up with
w^2 + 6w +5 = 0
That can be easily factored for the other two roots, which are both real.