A Wordy Sum!

I am assuming that you can multiply a number by itself a non-integral number of times, or else this problem is unsolvable.

The first sentence tells us that $\left(\dfrac{5}{2}\right)^x=1000$

The second sentence tells us that $\left(\dfrac{1}{40}\right)^y=1000$

Converting these to log form, we have $\log_{\frac{5}{2}} 1000=x$ and $\log_{\frac{1}{40}} 1000 = y$

This means $\dfrac{1}{x}=\log_{1000}\dfrac{5}{2}$ and $\dfrac{1}{y}=\log_{1000}\dfrac{1}{40}$

So $\dfrac{1}{x}-\dfrac{1}{y}=\log_{1000}\dfrac{5}{2}-\log_{1000}\dfrac{1}{40}=\log_{1000}\left(\dfrac{\frac{5}{2}}{\frac{1}{40}}\right)=\log_{1000}100=\dfrac{2}{3}$

And our answer is $2+3=\boxed{5}$ .