Please check this.
f(x)= 1/(x-1)^2 - 5
D= all real numbers, x does not equal to -5
R= all real numbers, y does not equal to 1
domain is all reals except where the denominator is zero
So, if you have
1/(x-1)^2 - 5
D= all reals except x=1
Clearly, 1/(x-1)^2 is smallest when x is huge. Then it is close to zero, but always a little bit positive. So,
R= all reals y > -5