Will moving the MATCH...AGAINST part in different part of the query (e.g. before evaluation of JOIN) will improve the performance?
I am glad you came here. I have always suggested using FULLTEXT indexes to collect keys first and then join it to other tables.


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In your particular case, I would suggest rewriting your query as an all-out JOIN:

SELECT t.* FROM tracking t
INNER JOIN tracking_items ti ON t.id = ti.tracking_id
INNER JOIN (SELECT car_id,car_text FROM cars WHERE MATCH(car_text)
AGAINST ('+bulgaria +turkey' in boolean mode)) c
ON ti.tracking_object_id = c.car_id LIMIT 5;


or maybe

SELECT t.* FROM
(SELECT car_id,car_text FROM cars WHERE MATCH(car_text)
AGAINST ('+bulgaria +turkey' in boolean mode)) c
INNER JOIN tracking_items ti ON c.car_id = ti.tracking_object_id
INNER JOIN tracking t ON ti.tracking_id = t.id  LIMIT 5;


If these queries give you an idea, please incorporate it if you still want to use WHERE EXISTS.

Please run the explain plan on these queries and your and see the differences

EXPLAIN select `t`.*
from `tracking` `t` 
where exists 
(   
    select `ti`.`id` from `tracking_items` `ti`
    inner join `cars` `c` on (`c`.`car_id` = `ti`.`tracking_object_id`)
    where `t`.`id` = `ti`.`tracking_id` and match(`c`.`car_text`)
    against('+bulgaria +turkey' in boolean mode) 
    limit 1
) and ... limit 5;

EXPLAIN SELECT t.* FROM
(SELECT car_id,car_text FROM cars WHERE MATCH(car_text)
AGAINST ('+bulgaria +turkey' in boolean mode)) c
INNER JOIN tracking_items ti ON c.car_id = ti.tracking_object_id
INNER JOIN tracking t ON ti.tracking_id = t.id LIMIT 5;

EXPLAIN SELECT t.* FROM tracking t
INNER JOIN tracking_items ti ON t.id = ti.tracking_id
INNER JOIN (SELECT car_id,car_text FROM cars WHERE MATCH(car_text)
AGAINST ('+bulgaria +turkey' in boolean mode)) c
ON ti.tracking_object_id = c.car_id LIMIT 5;


Give it a try, and let us know what happens !!!