Install SQL Express 2005 over 2012

You should instead use a version of SQL Server that is still supported. Also, SQL Server 2005 is not supported on Windows Server 2012.

Sorry.

If, for whatever reason, you have to have 2005, you'll need Windows server 2008 or 2008 R2. You'll have to copy the installer onto the Amazon EC2 instance and install it over remote desktop.