Mysql – How to improve the performance of this MySQL query

This query takes a long time to run, is there be a way I could rewrite it to make it faster?

SELECT DISTINCT r.racedate, re.trainerid
FROM raceentry re
INNER JOIN race r ON r.raceid = re.raceid
WHERE re.trainerid IS NOT NULL
AND re.Trainer30in90Starts IS NULL
AND re.trainerid IN (
    SELECT DISTINCT trainerid
    FROM pp_entries
)
AND re.raceid IN (
    SELECT re2.raceid
    FROM raceentry re2
    INNER JOIN race r2 ON r2.raceid = re2.raceid
    WHERE re2.horsename = re.horsename
    ORDER BY r2.racedate DESC
)
ORDER BY r.racedate DESC, re.trainerid LIMIT 500

This is what it displays when I run the EXPLAIN on it:

1   SIMPLE  pp_entries  NULL    range   IX_pp_Entries_1,trainerid               trainerid   5   NULL    4835    46.66   Using where; Using index; Using temporary; Using f...
1   SIMPLE  re          NULL    ref     PRIMARY,IX_RaceEntry,ix_RaceEntry_Horse,RaceEntry2...   RaceEntry_trainerID     5   thefigures_dbo.pp_entries.trainerid     10  10.00   Using where
1   SIMPLE  r           NULL    eq_ref  PRIMARY,IX_Race     PRIMARY     17  thefigures_dbo.re.RaceID    1   100.00  NULL
1   SIMPLE  r2          NULL    eq_ref  PRIMARY,IX_Race     PRIMARY     17  thefigures_dbo.re.RaceID    1   100.00  Distinct
1   SIMPLE  re2         NULL    eq_ref  PRIMARY,IX_RaceEntry,ix_RaceEntry_Horse,RaceEntry2...   PRIMARY     49  thefigures_dbo.re.RaceID,thefigures_dbo.re.HorseNa...   1   100.00  Using index; Distinct

Thanks guys, used a combo of the suggestions and ended up with this query

SELECT DISTINCT r.racedate, re.trainerid
FROM raceentry re
INNER JOIN race r ON r.raceid = re.raceid
WHERE re.trainerid IS NOT NULL
AND re.Trainer30in90Starts IS NULL
AND re.trainerid IN (
    SELECT trainerid
    FROM pp_entries
)
LIMIT 300

The biggest improvement seemed to be removing the 2nd IN() clause suggested by Oreo