You only get 2 MySQL databases with the Free Hosting plan (see the plan comparison page). You can step up to a paid plan, or participate madly in the forum in a productive way (gaining reputation points along the way) to make it to a user group that gets additional features.
Or you can use application-specific table prefixes (something most forum and CMS software allows, and that is easy to build into your own custom development) to use one database to service more than one application.