Please note that there's a 5.1.4 patch set available, so you should really consider upgrading to that version as opposed to 5.1.3 - that's if upgrading to 18.1 is too big a step to take. At least move to the most recent 5.1.x patch set available.
What steps are you following to actually upgrade your APEX 4.2 instance to 5.1.3? You've mentioned an import/export but I see no mention of an actual upgrade. As part of an APEX upgrade, we will detect that you've already got the Packaged App installed, and expose an 'Upgrade' button to you in the upgraded 5.1.x instance. However, it doesn't sound like you're doing an upgrade, and instead just moving the schema to an instance running APEX 5.1.3. If you are hitting the 'Prerequisite Check Failed' error, then it sounds like you ran the 'Install' option for the Packaged App in your new 5.1.3 instance, and therefore the instance didn't detect that you already have the app installed. I would recommend reviewing our Installation Guide, and ensure you're following the correct steps to upgrade your instance: https://docs.oracle.com/database/apex-5.1/HTMIG/toc.htm