How can I speed up MySQL query with multiple joins

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Here is my issue, I am selecting and doing multiple joins to get the correct items...it pulls in a fair amount of rows, above 100,000. This query takes more than 5mins when the date range is set to 1 year.

I don't know if it's possible but I am afraid that the user might extend the date range to like ten years and crash it.

Anyone know how I can speed this up? Here is the query.

SELECT DISTINCT t1.first_name, t1.last_name, t1.email 
FROM table1 AS t1 
INNER JOIN table2 AS t2 ON t1.CU_id = t2.O_cid 
INNER JOIN table3 AS t3 ON t2.O_ref = t3.I_oref 
INNER JOIN table4 AS t4 ON t3.I_pid = t4.P_id 
INNER JOIN table5 AS t5 ON t4.P_cat = t5.C_id 
WHERE t1.subscribe =1 
AND t1.Cdate >= $startDate
AND t1.Cdate <= $endDate
AND t5.store =2

I am not the greatest with mysql so any help would be appreciated!

Thanks in advance!

UPDATE

Here is the explain you asked for

id  select_type     table   type    possible_keys   key     key_len     ref     rows    Extra
1   SIMPLE  t5  ref     PRIMARY,C_store_type,C_id,C_store_type_2    C_store_type_2  1   const   101     Using temporary
1   SIMPLE  t4  ref     PRIMARY,P_cat   P_cat   5   alphacom.t5.C_id    326     Using where
1   SIMPLE  t3  ref     I_pid,I_oref    I_pid   4   alphacom.t4.P_id    31   
1   SIMPLE  t2  eq_ref  O_ref,O_cid     O_ref   28  alphacom.t3.I_oref  1    
1   SIMPLE  t1  eq_ref  PRIMARY     PRIMARY     4   alphacom.t2.O_cid   1   Using where

Also I added an index to table5 rows and table4 rows because they don't really change, however the other tables get around 500-1000 entries a month... I heard you should add an index to a table that has that many new entries....is this true?

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