What version of SQL Server are you using?
What is the SQL Server client installed, ODBC 13 is to be used with 10.5. Microsoft SQL Server database requirements for ArcGIS 10.5—Help | ArcGIS Desktop
Well that is the problem. The last time that SQL Server 2005 was supported was back at 10.0. ArcGIS 10 System Requirements
It stopped being supported and the minimum SQL Server version was 2008 with the 10.1 release. System Requirements
I had the same "Stream Finished" error when I upgraded from 10.3.1 to 10.6 and tried to connect to our old SQL2005 servers. I uninstalled 10.6 and found that I could connect to the database with 10.4.1 and 10.4 installed, but although I could view data, some processes (e.g. Table to Table with a Where statement) would still fail. I rolled back again to 10.3.1 and everything is working again. As George said, I suspect this is more luck than anything else and I wonder if there is other functionality that is not working that I have not noticed (yet). For now though, I'm going to have to stick with 10.3.1 until we can get our 2005 SQL servers upgraded.