A happy new year to you too (and everyone who reads this, of course). What you’re describing sounds to me like exactly what restic does. When you create a snapshot, you will be able to restore exactly what all your files were like at that moment.
Also, restic does deduplication. So if a file has not changed, it is not being stored multiple times. Even better: restic deduplication works on parts of files too. So if a very large file has changed, only the changed part will be saved in the new snapshot.
The question how long you can backup 5 TB of data to a 6 TB drive depends on how much that data changes. You can increase that time by periodically deleting snapshots - forgetting and pruning them in restic speak.