Hi Jo.
Back up the database from the 5.1 server, and restore it to a TSM server running 5.3, then upgrade that to 5.5. Direct upgrades are generally supported from X-2 ("X minus 2") versions, where X is the 'current version'. (So, from TSM 5.3, X-2 is 5.1. Then, from TSM 5.5, X-2 is 5.3.)
-JD.