f(-1)=-1+5-17+13=0 so x=-1 is a zero and we can reduce the cubic to a quadratic by synthetically dividing it by the zero:
-1 | 1 5 17 13
1 -1 -4 | -13
1 4 13 | 0 = x2+4x+13, which has complex zeroes.
x2+4x=-13,
x2+4x+4=4-13=-9 (completing the square),
(x+2)2=-9, x+2=±3i, x=-2+3i, -2-3i.
SOLUTION
Zeroes are -1, -2+3i, -2-3i.