I'm not sure what part log shipping plays in your upgrade.
The steps you should take are:
- Install SQL 2005 on a new server.
- Take your production system offline.
- Perform a backup.
- Restore the backup to the new server.
- Attach your production system to the new server.
- Test..test..test.
After you've moved it over, you might consider changing the compatibility level of the database in the new server to SQL 2005. However, be aware that there are many differences between SQL 2000 and 2005. So review this: http://technet.microsoft.com/en-us/library/ms143232(v=sql.90).aspx to get an idea of what issues you might have.