Trying to revive an old wordpress site, but newer versions of wordpress install a different db structure

I'm trying to revive a site that worked in 2015. The theme is custom, and contains custom post types, pages, and a bunch of standard posts.

When I use Wordpress 4.4 (the version that this last worked on), the PHP in Wordpress core is too old to work (get_magic_quotes_gpc() has been deprecated, amongst other things, I'm sure). When I install the current version of Wordpress, it ignores my tables, and installs the familiar Wordpress empty tables alongside them, but with wpn3_ prefixes, instead of wp_, and the site behaves as a fresh install.

How do I remedy this? Can I just rename my tables to the new prefix? Or is there some sort of conversion process to get the old pages/metas in to the new?