There are n horses. At a time only k horse can run in the single race. How many minimum races are required to find the top m fastest horses? Please explain your answer. (There is no timer.)

This was asked and not (yet) answered at math.stackexchange.

The $n = 25, k = m = 5$ case was a Google interview question and there are various answers on the web. But I am not sure what should be the right answer for this. Any ideas?