Query slow - not using relevent indexes
According to my knowledge of indexes (i haven't work with MySql lately), first: whatever field you have in your LIST of SELECT should also be indexed.

But i noticed another probable behavior that could be happening in your given query: in your INs you are looking for strings ('1', '2', 'etc'), are those fields Varchars, Chars?.

If not, try to use INT instead of STRING, if your "product_family_id" is INT and you are doing "product_family_id IN ('1','2') the engine executes an implicit conversion, resulting in more executon time.

If "product_family_id" is string and you are storing numbers as text. and if you only have numbers stored in there (as string though) then try to cast to int

cast(product_family_id as int) IN (1,2,3,4,5)


Try both solutions. Add an Index to the select list members, use numbers instead of text. and try casting as well.