I then installed SQL Server 2008 Express on my machine and elected to have it install SQL Server Management Studio Basic.
I uninstalled 2005 and SQL Server Management Studio Express.
I was able to connect with no problems to my PC-NAME\SQLEXPRESS instance (no, PC-NAME is not my computer name -). I previously had 2005 on here and used it just fine with the old SQL Server Management Studio Express. I just installed SQL Server 2008 Express on my Vista SP1 machine.