The 'authentication' part of the error message is to do with the way that your mySql password has been written to the root (admin) mySql database on your server (which you probably don't have root user access to). This may have been set up before the hosting server system's upgrade to mySql v.5x.
Are you able to create a new database user via your control panel? If so, as a test, create a new user (with full permissions), this will also create a new password. Try setting up a connection using your new user name in Dreamweaver and try connecting again.