Let two numbers be a and b. a*b=-500 and a+b=5, so a=5-b, which can be substituted into the product:
b(5-b)=-500; b^2-5b-500=0, a quadratic equation. Factorise: (b-25)(b+20)=0, so b=25 or -20. The two solutions are a and b, so the numbers are 25 and -20.