> f:= x -> (x^2+1)/(x-5);

> L:=[m, 5-10^(-m), f(5-10^(-m))];

> for m from 0 by 1 to 10 do print(evalf(L)); od;

The evidence appears to indicate that the limit is - infinity.

In fact, this is corraborated by Maple:

> limit(f(x),x=5,left);