A logic problem by Payal Sheth

There are 25 horses. You have to get first 3 fastest horses out of all 25 by making some number of matches between them.

Rule 1: You have no gadget to count the time taken.

Rule 2: Only 5 horses can run on the track (ground) at one time.

What is the minimum number of matches you will have to conduct to choose these 3 fastest horses?

Hint 1 : Try and eliminate as many horses as possible.

Hint 2 : The horse which comes 2nd in one match can be possibly faster than the winner of 2nd match (when you divide the horses in groups of 5 and arrange matches.)