As part of our migration from Exchange Server 5.5 to Exchange Server 2003, we want to install Exchange servers in our root Active Directory (AD) domain. What permissions are required to do this?

The account you use to install Exchange 2003 or Exchange 2000 Server must be a member of the Domain Admins group for the target domain. So, if you're installing the servers into the root domain, you'll need to add the account that you're using to perform the installation into that domain's Domain Admins group.