That is a possibility, however, my recommendation would be to remove SQL
Server and install from scratch.  Just my personal preference.

However, here is are the upgrade options and some notes on about edition
upgrades

http://msdn.microsoft.com/en-us/library/ms143393.aspx

Upgrade Notes

After upgrading to SQL Server 2005 from another edition of SQL Server 2005,
you must re-apply any hotfix or service pack updates to the upgraded SQL
Server instance.

Cross-version instances on SQL Server 2005 are not supported. Version
numbers of the Database Engine, Analysis Services, and Reporting Services
components must be the same within an instance of SQL Server 2005.

Before upgrading to SQL Server 2005, enable Windows Authentication for SQL
Server Agent and verify that the SQL Server Agent service account is a
member of the SQL Server sysadmin group.

Before upgrading from one edition of SQL Server 2005 to another, verify that
the functionality you are currently using is supported in the edition to
which you are upgrading. For more information, see the section for your
components in Features Supported by the Editions of SQL Server 2005.

Thanks Ross