Help!! I'm stuck with this limit. Limx-->5(from the positive end) (1/ln(x-5)

Question

I have tried using math calculators like symbolab and wolframalpha but they all cannot compute when I put the limit from the positive end. I know the answer is either 0 or DNE. But I cannot work it out.

Answer 1

domain of this function is all real numbers but x≠5

 

the limit of F(x) approaching from 5⁺ is positive ∞

 

 

the limit of F(x) approaching from 5^- is positive -∞

 

the overall limit DNE because the left side limit does not equal the right side limit