Let me guess. 15 is the one not being shown, 3 still appears? Your query is just written inproperly. Try either of the following; they both work.
SELECT topic_id, topic_title, topic_views from realm_topics
WHERE forum_id NOT IN('15','3')
ORDER BY topic_id desc LIMIT 5
or
SELECT topic_id, topic_title, topic_views from realm_topics
WHERE forum_id !=15 AND forum_id !=3
ORDER BY topic_id desc LIMIT 5
Cgraz