w³ + 5w² - w = 5

Get 0 on the right by adding -5 to both sides:

     w³ + 5w² - w - 5 = 0

Factor w² out of the first two terms on the 
left and factor -1 out of the last two.

 w²(w + 5) - 1(w + 5) = 0

Factor (w + 5) out of both terms:

      (w + 5)(w² - 1) = 0

Factor the second factor as the difference
of two squares:

(w + 5)(w - 1)(w + 1) = 0

Set each factor = 0.

Setting w + 5 = 0 gives w = -5
Setting w - 1 = 0 gives w = 1
Setting w + 1 = 0 gives w = -1

The three solutions are -5, 1, and -1

Edwin