Question 694244
You need to also have as zeros the conjugates of those numbers: {{{5+i}}} and {{{-sqrt(17)}}}.
That way, when you multiply factors involving conjugates, the irrational/imaginary parts cancel out.
Your polynomial must be of grade 4, and the one with a leading coefficient of {{{1}}} can be calculated as:
{{{((x-sqrt(17))(x+sqrt(17)))((x-(5-i))(x-(5+i)))=(x^2-17)((x-5+i)(x-5-i))=(x^2-17)((x-5)^2-i^2)=(x^2-17)(x^2-10x+26)}}}.
I left the last multiplication for you to do.