How to make SQL Server Management Studio use latest version of SQL Server?
Microsoft SQL has several components.  You can install SQL Studio (the GUI you're using), SQL Server itself (the actual database, to which SQL Studio can connect), Analysis Services, Reporting Services, and others.

You currently have a SQL 2005 server running, and you're connecting to it with SQL Studio 2012.  That's OK!  But if you'd rather have a SQL 2012 database on your local machine, you will need to run the SQL 2012 installation process again, and add that component.  You may want to remove the 2005 installation first (backup your database first, of course).

If you've used WAMP or LAMP, what you have is equivalent to installing different versions of MySQL (the database) and PHPMyAdmin (the GUI).  Or Oracle and Toad.