Thank you stephenwaite, your procedure worked with the following modifications but essentially the concept is the same. I got it to work the following way if someone else needs to do the same:
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Install openemr 5.0.0 on the new server. Make sure you can login and ensure correct installation.
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Make a backup on the 4.1.0 machine with either the backup tool in OpenEMR or the procedure at
https://www.thegeekstuff.com/2008/09/backup-and-restore-mysql-database-using-mysqldump/
The backup tool makes a compressed file emr_backup.tar that contains openemr.sql -
Transfer the openemr.sql to the 5.0.0 server and restore the database using the steps in 2
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Follow the upgrade process in http://www.open-emr.org/wiki/index.php/Linux_Upgrade_4.2.2_to_5.0.0
to move all the correct folders from the 4.1.0 server to the 5.0.0 server. -
Run the sql.upgrade.php script and select the correct version you are upgrading from.
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You should now be able to login on the 5.0.0 server with all the data transferred