What is the lowest output value approached by the function f(x)=2x−5?

Are you sure you wrote it right?  :-(

The function f(x)=2x-5 is a linear function.

Unless otherwise stated (and that does not seem to be the case) in the real numbers domain, x may assume any value.

The same can be said to y.  

So, the lowest output value approached by this function is -∞

(minus infinity).

:-)