I am currently running ArcGIS Server 10.1 enterprise geodatabase with SQL server 2008. My goal is to migrate to ArcGIS Server 10.5 with SQL server 2014 (my IT’s current standard). I am trying to determine the order in which to do this because AGS 10.1 is not compatible with SQL Server 2014 and AGS 10.5 is not compatible with SQL Server 2008. Can someone assist with laying out the steps with these compatibility issues?
So you mention your IT department's current standard which mean I will assume you have a SQL DBA.
Have DBA perform a backup of existing DB you have in SQL 2008. Restore the backup into SQL 2014 (don't forget to address user accounts so you don't get orphans). Using 10.5 Catalog log into the SQL 2014 DB. Perform upgrade of 10.1 to 10.5.
Sorry for short explanation running out the door but that's the route I'd go down and we've moved multiple databases multiple times from 10.0 through 10.5 now on SQL 2005 - 2016