Logical Question: Find fastest 3 horses out of 25.

There are 25 horses among which you need to find out the fastest 3 horses. You can conduct race among at most 5 to find out their relative speed. At no point you can find out the actual speed of the horse in a race. Find out the minimum no. of races which are required to get the top 3 horses.

[anirudhkharayat]

sir if we make horses race in random order (taking any 5 horses) then take the fastest among them and make the fastest race among them selves then the minimum number of races should be 6 can you please tell what is wrong with my logic