Hi Pete,
If possible the best thing to do here would be to upgrade your server version of PHP to at least 5.4.
This should be possible using your hosts control panel, and if not you can ask your host if they will do this for you.
Since it looks like you are restoring onto a different websever (presumably with a different URL) then you should tick the option to search/replace the database, which appears when selecting to restore the database. This will change all of the URLs inside the database to point at the new website, rather than to the old one.
Best wishes,
Luke