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The factor pairs of 90 are (90,1)(45,2)(30,3)(18,5)(15,6)(10,9)

None of them differ by 5.

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An updated answer

The quadratic equation

has the solutions

Assuming the two numbers are x and y; then:
xy = 90, or y = 90/x .............................................. 1
x + y = -5 ............................................................. 2
Substituting from 1 into 2 results in:
90/x + x = -5
or
x2 + 5x + 90 = 0 where a = 1, b = 5, and c = 90
Then:
From the formula above:
x = (-5 +/- (25 - 360)1/2 )/2

x = [-5 +/- (-325)1/2 ]/2 = [-5 +/- 18.0278 i]/2

accordingly x = -2.5 + 9.0139 i or -2.5 - 9.0139 i where i = (-1)1/2
Substitute in equation 1 you get the value of y as
y = 90/x

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