Auto archiving between 2 document libraries on one site

I want to implement auto archiving from one document library to another document library on the same site, because of the size of the first library (>5000), so the users of this library can use the synchronize option again. I prefer to use a different document library on the same teamsite as archive and do not want to use a method which copies, pastes and deletes the documents but instead I want to move them. I searched for an easy way to do this, but so far I only found solutions around record management that are not easily implemented and may limit the user of the teamsite by for example enforcing them first check out all the documents they want to edit.
Any ideas on how to solve this problem?