So you've got 2003 & 5.5 and you still have your BESAdmin account located on the 5.5 server? What version of 5.5 and what version of 2003 ... give this a gander too:
5.5 to 2003 migration ... do you have this planned?
... and YES, move your BESAdmin mailbox to the 2003 server and upgrade your components ... do any of the users on your 5.5 server have problems with syncing not working properly?