25 horse, 5 tracks, find 3 fastest horses

We have 25 horses, and we want to pick the fastest 3 horses out of those 25.
We have only 5 tracks. Means, in each race, only 5 horses can run at the same time.

What is the minimum number of races required to find the 3 fastest horses without using a stopwatch?
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Answer:
7

First 5 race should be held among 25 horses.
6th race should be held among... winner of every race.
7th race should be among...
( Second and Third horses from the group of first winner of 6th race,
  top two horses from the group of  second winner of the 6th race,
  top horse from the  group of third winner of 6th race. )