Possible roots are the factors of 20: {1, 2, 4, 5, 10, 20} and their negatives.
Use synthetic division. For example, if I chose 4 as a possible root, the synthetic division setup would be
____________
4 / 1 -4 -5 20
4 0 -20
_____________
1 0 -5 0
This tells us that 4 is a root (I was just lucky) and (x-4) is a factor.
The quotient (remaining factor) is (x^2 - 5), which, if factored, yields
x = sqrt(5) and x = -sqrt(5)
In summary, the roots (or zeros) of f(x)= x^3-4x^2-5x+20 are
{sqrt(5), -sqrt(5), 4}