Generally compound fractions are annoying. This is just one way to do the problem, but it will be much easier if you get rid of them. You have a y on the bottom of one fraction in the numerator, and a 5 on the bottom of the other. So multiply the whole thing by (5y)/(5y) to take care of both of them. Then you are left with
(5-y)/[ 5y (y-5)]
(5-y) / (y-5) = -(y-5) / (y-5) = -1.
You are left with 1/(5y), which is continuous at 5, so you can substitute 5 in for y to take the limit.
(Side note, always write 1/(5y), never 1/5y.)