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You can see that the sum of the coefficients on the left side is zero. This means 1 is a root, and (x-1) is a factor.
The remaining roots will be solutions to the quadratic equation
(x^3 - x^2 - 5x + 5)/(x - 1) = x^2 - 5 = 0
This has roots
x^2 = 5
x = ±√5
The remaining roots will be solutions to the quadratic equation
(x^3 - x^2 - 5x + 5)/(x - 1) = x^2 - 5 = 0
This has roots
x^2 = 5
x = ±√5
The solutions are x = {-√5, 1, √5}.
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