How do I backup and restore a 4.1.9 instance to a new cluster running 5.1.x ?

Hello,
We've finally got to the stage where we can migrate an existing 4.1.x instance to new hardware (with a different naming convention). The backup.sh script is fine if restoring to the original hosts but not to new ones.

Is there an approved (or at least tested) way of doing this ?

Many thanks
Pete