Restoring differential backup from SQL Server 2005 to SQL Server 2012
There should be no issue restoring differentials and fulls from SQL 2005 to SQL 2012.  I would validate that your backup files are compatible.  To do this, you'll want to use the RESTORE HEADERONLY command and compare the full backup's FirstLSN value with the differential's DifferentialBaseLSN:

restore headeronly
from disk='X:\BackupFiles\foo.bak'




If these values do not match, then you will need to take an appropriate full backup.