Question

What numbers add up to -5 and multiply to get -90

Answer 1

You don't say how many numbers you want to do that with.

If you want just two numbers, then they're  +7.3107  and  -12.3107 .
(Those are rounded, not exact.)

I took a quick look among the factors of 90, looking for sets of 3 numbers
that would do it, and I couldn't find any.

Answer 2

Let
x-------> the first number
y-------> the second number

we know that

$x+y=-5 \\ x=-5-y$ equation 1

$x*y=-90$ equation 2

substitute the equation 1 in equation 2

$[-5-y]*y=-90 \\ -5y- y^{2} =-90 \\ y^{2} +5y-90=0$

using a graphical tool to resolve the second order equation
see the attached figure
the numbers are
-12.311
7.311