g(x)= 

We just have to leave out the values on the x-axis 
where there are vertical asymptotes:

That is where the denominator = 0

(x + 5)(x - 1) = 0
x+5 = 0  x - 1 = 0
  x = -5     x = 1

The graph is below. Notice that the function does not use 
the values of x where there are vertical asymptotes (where 
the green lines, the asymptotes cross the x-axis


  
<=========o=================o===========>
-8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4
Notice this number line representing the domain.
Compare it to the x-axis above. It is just like it!
Its interval notation is

        

That's the domain.
Edwin