I have the exact same problem. The closest solution I can think of is a little hacky, and it definitely is not great if you will be doing this import often.
My solution is to use WP All Import to import new posts for each image, so that each image gets uploaded to your media library. This will also create 5000 garbage posts, but you can delete them afterwards. I would suggest uploading the new posts as drafts so that they don’t appear on the website when you do the import.
Let me know if you found a better solution.