Restoring .bak file SQL Server 2005 in SQL Server 2008
All restore operations in SQL Server are backward compatible. You can restore a 2005 backup on a 2008 instance just like you would restore a 2008 backup on that same instance.

There are some limitations to older SQL Server versions, but a backup that was taken on a 2005 or newer instance can currently be restored on any supported SQL Server version.

However, the backups themselves are not backwards compatible. So on a 2005 instance you cannot restore a backup that was taken on a 2008 instance.