(1) Back up the transaction log
(2) Restore the Full from 05/11 with no recovery
(3) Restore the differential from 11/11 with no recovery
(4) Restore all transaction log backups since the 11/11 differential and recover
Then...
(5) Test regularly that you can restore from your backups so that stuff like this doesn't take you by surprise
If your database is in Simple recovery mode, or you don't have any (or all) transaction log backups, then you'll only be able to restore to the 11/11 differential, or to the log backup before the first one that's missing.
John