SOLUTION: Approximate the limit from a graph of the function, and then find the limit algebraically. Thanks!
{{{matrix(2,1,lim,"x->5")}}}{{{(sqrt(x)-2)/(x-5)}}}
The limit does not exist because the denominator approaches 0
as x approaches 5, but the numerator approaches a finite number.
There is an asymptote on the graph of at 5, (the green dotted line).
Edwin