When we look at each function we can see that g is defined for all values of x as a linear function. It is represented by an infinitely long straight line. But f is the square root of g(x) when the two functions are combined. We can't find the (real) square root of a negative number so the domain must be limited. What we need to find out is: when is g(x) negative? To answer this we put g(x)=2x-5<0 and solve for x. 2x<5, so x<2.5. These are values of x we need to avoid. The domain for the combined function f of g is therefore x>2.5.
The context of your question has g(x)=2x+5, so g(x)=2x+5<0 when x<-2.5 and the domain of x needs to avoid these values, so x>-2.5. Check which is correct: the title for your question or the context.