#### Answer

$f(x)=-x^{2}-10$ and $g(x)=-x-5$

#### Work Step by Step

We know that $(f-g)(x)=f(x)-g(x)$.
Therefore, we know that the two polynomial functions will have to satisfy the following condition:
$f(x)-g(x)=-x^{2}+x-5$
Two such functions that satisfy this condition are:
$f(x)=-x^{2}-10$ and $g(x)=-x-5$
$f(x)-g(x)=(-x^{2}-10)-(-x-5)=-x^{2}+x-10+5=x^{2}+x-5$