Is it possible for the chain rule to be required when finding the derivative of a fraction

Because I just solved (2x+5)/x^2 and a derivative calculator is telling me the answer is -2(x-5) / x^3. Why didn't I have to chain on the derivative of the numerator?

The derivative calculator is wrong.

Quotient Rule:
d/dx[ (2x + 5)/x^2 ]
(2x^2 - 2x(2x + 5)) / x^4
(2x^2 - 4x^2 - 10x) / x^4
(-2x - 10)/x^3
-2(x + 5)/x^3

It seems it should be +5 not -5

I'll also do it using the Product Rule:
d/dx[ (2x + 5)x^-2 ]
2x^-2 - 2(2x + 5)x^-3
2/x^2 - (4x + 10)/x^3
Now to get it to look like the quotient rule answer:
2x/x^3 - (4x + 10)/x^3
(2x - 4x - 10)/x^3
-2(x + 5)/x^3