Those are not databases but SQL Server instances. The first is default with SQL Server 2008 and the second with SqlExpress 2005. Most likely SqlExpress has been installed by a Visual Studio

You have to ununstall the second one if you want to get rid of it.
Another option is to disable service for SqlExpress so it'll not run

>
>When I run SSMS I can select one of two databases:
>1. The same name as the computer (MyComputerName) and the version says 10.0.5500
>2. MyComputerName\SQLEXPRESS. Version 9.0.1399
>
>Since the first one is higher version number, do I understand that I can remove/delete the SQLEXPRESS (of earlier version)? If so, how do I remove it?
>
>TIA