Classic 25 Horse Problem

Classic 25 horse problem,
25 Horses,
Have a 5 horse track,
No stopwatch,
How many races are required to determine the 3 fastest horses?

Answer : 7 Races

And here goes why? 

1. we have 5 races for 25 horses that 5 horses on a team, define each team as a, b, c, d, e.
2. carry a best horse race for each team first place, define them as a.1,b.1,c.1,d.1,e.1
3. assume prior best horse race 's top 3 places are a.1 b.1 c.1 , so we know the fastest horse is a.1
4. we only need to take last race to know who are second and third quickest horse.
5. The horses that participate in this race are b.1 b.2 a.2 a.3 c.1 , this race 's top 2 places are 2nd and 3rd quickest horses