There are overlaps in the version numbers between UBB-Classic (Perl/cgi-bin) and UBB.threads (PHP). This has caused some confusion in the early years. The naming of the former version from "UBB" to "UBB-Classic" was intended to reduce much of that confusion.
You were able to run UBB-Classic on a server running php 5 because UBB-Classic did not use PHP. It used a flat file system for users and posts. no SQL databases at all.
Once you move away from UBB-Classic, you will be able to upgrade from UBB.threads 7.5.6 directly to UBB.threads 7.7.0.
I'm still working on 7.7.0 as we speak. there is a dependence on an major asset that was not written by UBB, but that ubb heavily relies on. I mention this because that asset is compatible with PHP 7.0 and PHP 7.1, but not PHP 7.2. This is still all being worked out as UBB.threads version 7.7.0 is continuing its development. Many things may or may not change over this next major version.