Well, let's clarify. "5 of the most recent submissions" is quite a different matter than "THE 5 most recent submissions", so which is it?
For the former:
select * from table order by col_date desc limit 5;
will do. You will get no more than 5 rows, and their dates will not be earlier than any non-displayed rows. (Notice the careful weasel-words.) But if you really want THE 5 MOST RECENT, you can't do without an autoincrement column. Then you say:
select * from table order by unique_id desc limit 5;