How Many Races to Find the Top 3 Horses from 25 with Only 5 Tracks?

[Albert1]

you have 25 horses and you have to pick fastest 3 out of the 25. In each race
only 5 horses can run at the same time as there are only 5 tracks. what is the
minimax number of races to ensure the 3 horses can be chosen without using a stopwatch ?
(suppose the speeds of all horses are different)

 

[Albert1]

you have 25 horses and you have to pick fastest 3 out of the 25. In each race
only 5 horses can run at the same time as there are only 5 tracks. what is the
minimax number of races to ensure the 3 horses can be chosen without using a stopwatch ?
(suppose the speeds of all horses are different)

my solution:

Spoiler

after each race two horses will be eliminated from competition ,
so when race 8 is finished ,there are only 9 horses remained marked with $A_1,A_2,A_3,A_4,A_5,A_6,A_7,A_8,A_9$
we arrange race 9:$A_1,A_2,A_3,A_4,A_5$
race 10: $A_1,A_2,A_3,A_6,A_7$ $(A_4,A_5)$ out from race 9
race 11:$A_1,A_2,A_3,A_8,A_9$ $(A_6,A_7)$ out from race 10
after race 11 the top 3 can be produced
$25-11\times 2=3$