I have seen the same behavior with ArcGIS Desktop 10.2, and SQL Server 2005.
I am not going to take the time to find it now, but there is documentation stating that ArcGIS Desktop 10.2 is compatible with SQL Server 2005. I am currently using the two products together.
SQL-Server 2005 was released nearly nine years ago (with the last service pack issued four years ago), and I haven't found any indication that Microsoft is still supporting it either. According to the 10.1/10.2 Deprecation Plan (p. 7 of 10), enterprise geodatabases are not supported with SQL-Server 2005, starting at 10.1:
Three major releases is usual for Esri RDBMS support (2008, 2008R2, and 2012). Reverse compatibility on drivers may extend the use of elderly database products, but they remain unsupported (If they work, fine, but if they don't, there isn't anything that can be done).
To add to what Vince mentioned above, ESRI *does not restrict\prevent* customers from connecting to a SQL Server 2005 geodatabase. ESRI does not support connections from Desktop 10.1 and later releases, to a SQL Server 2005 geodatabase.
Thus even though you will be able to connect just fine, you may encounter inconsistencies down the line.
When looking for documentation regarding compatibility and System requirements, I believe the below links should always be preferred..
System Requirements (10.1)
System Requirements (10.2.x)
The supported database versions are very clearly mentioned at the beginning of these links.