Question

P(x)= P has degree 3 and zeros 5 and i.

Answer 1

Keeping in mind that complex solutions never come all by their lonesome, they always come with their sister

thus, "i" is not there all by herself, her sister is there too, namely the conjugate

so
i = 0+i     and thus its conjugate sister will be  0-i

thus    $\bf \begin{cases} x=5\to &x-5=0\\ x=0+i\implies x=i\to &x-i=0\\ x=0-i\implies x=-i\to &x+i=0 \end{cases} \\\\\\ (x-5)(x-i)(x+i)=\textit{original polynomial}$