There are 25 horses, each one runs at constant speed and each one runs at different speed. You need to find out the minimum races it takes to find out

There are 25 horses, each one runs at constant speed and each one runs at different speed. You need to find out the minimum races it takes to find out the first, second and third fastest horses from them. Each horse race can only have 5 horses and you don't have a stop watch to time it.
First race each group which has 5 horses, take the winner of each group, and race them, then, drop the fourth and fifth horses, take the 2nd and 3rd from winner’s original group, and 2nd horse from 2nd winner’s original group, race them, get the other top 2 horses