If you have 25 horses and no timer, how many races would you have to run to figure out the top 5 fastest horses?

"Wow, I think I remember this one. My old professor posed this question to me a few years ago. To find the fastest, you'll need to race all twenty-five horses at least once. Racing five horses at a time, you need a minimum of twenty-five races, with five horses per race. Twenty-five divided by five equals five. Then you need to compare the winners of those races, which means one last race will be necessary to determine the fastest, so six races total to find a winner."