The safest way: Using the same server....
Is to upgrade to 5.1 - backup DB; upgrade to 5.2 - backup DB; then upgrade to 5.3 - backup DB.
The reason behind the separate TSM DB backups is in the event you have to fall back and need to restore the TSM DB.
Depending on the size of your current DB - upgrade times are not that lengthy or troublesome.
If you built a separate server = there will be no way to restore a TSM 4.1 DB into TSM 5.3 DB...there is too many changes in versioning.
Good luck
Steven