Possible, yes, but a really bad idea. Failover would work, providing you have no Enterprise-only features but you wouldn't be able to fail back.
DR should be the same version, edition, patch, everything as the primary. If you have 2005 primary, use 2005 as the DR.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability