First observe that x=-1 is a root of the equation. Use long division to divide x^3-3x^2+x+5 by x+1, we find that (x^3-3x^2+x+5)/(x+1)=(x^2-4x+5). Now we need to find the roots of x^2-4x+5. x^2-4x+5=0, x^2-4x+4=-1, (x-2)^2=i, x-2=i or -1, x=2+i or 2-i. The three roots are 2+i, 2-i, -1.
