To move the database you may perform the following:
Backup the current database
Restore the database into the new SQL server. You can restore from a lower version of SQL to a higher version SQL, but not the other way around. We are not aware of any issues when restoring a 2005 backup of a database onto a 2008 R2 (there were performance issues when restoring 2005 on 2008).
Run the console installer using the instructions linked to below, selecting to use an existing database, and entering the new database location and login credentials. Please ensure that the Console Administrator Tool, Server Manager, and any instance of SSMS connected to the database is not open when running the installer.
The following article has instructions for running the installer. Please ensure that you follow all of the steps, including all of step #15 'Additional Steps':