Unfortunately if you base your query on a date then
tempdb
will (usually) still appear in your list (depending on how the instance is being managed).
If you use the standard approach
select [name] from sys.databases where database_id > 4
then (in your case) you will still get entries for
ReportServer$SQLEXPRESS
and
ReportServer$SQLEXPRESSTempDB
. You can't just change the WHERE clause to
where database_id > 6
because if you
don't have Reporting services installed then you'll wrongly omit some genuine user created databases.
It may look as if you could use
select * from sys.databases where owner_sid = 0x01
i.e. list all databases created by the admin account. BUT what if your DBA used that account to create databases on behalf of a user? Again, you could wrongly omit some genuine databases of interest.
Probably the safest route is
select * from sys.databases where database_id > 5 and [name] NOT LIKE 'ReportServer%'