date_added сделайте. i, то по любому проиндексирован. Ещё можно и не active индекс повесить.
select distinct class_ads.*, class_ads.id as adid, date_format(class_ads.`date_added`,'%d.%m \320\262 %H:%i') as date_nice, date_format(class_ads.`date_expires`,'%d.%m \320\262 %H:%i') as date_expires_nice, UNIX_TIMESTAMP(class_ads.`date_added`) as `time_added`, (class_ads.date_expires < '2019-08-01 11:12:49' and class_ads.date_expires!='0000-00-00 00:00:00' and class_ads.active=0) as expired, class_slugs.slug from class_ads inner join class_slugs on class_ads.id=class_slugs.object_id where class_ads.active = 1 and class_slugs.`type`='listing' order by `viewed` desc limit 0, 6