Question 1080085
I'm assuming you mean with real coefficients so the complex roots are in complex conjugate pairs. 
However, that polynomial would only need 4 zeros to specify it so the fifth zero is arbitrary. 
I will make it 4th degree and you can check your problem setup and repost if necessary.
{{{f(x)=(x+1)(x-2)(x+i)(x-i)}}}
 {{{f(x)=(x^2-x-2)(x^2+1)}}}
{{{f(x)=(x^4-x^3-2x^2)+(x^2-x-2)}}}
{{{f(x)=x^4-x^3-x^2-x-2}}}
So for example, I can add {{{x=0}}} as a root,
{{{f(x)=x(x^4-x^3-x^2-x-2)}}}
{{{f(x)=x^5-x^4-x^3-x^2-2x}}}