I don't get enough notifications to see this, and I don't think I've got anything beyond 'show 5' anyway.
So, this is speculative. If you tap where it says "15 More" does it then show the 15 more?
One thing you can try is Settings > General > Reset > Reset All Settings. This defaults a lot of settings like wallpaper, sounds, etc. I'm not sure how it affects Notifications, but if it resets them (as it hopefully should) then you can go back and re-tweak to see if it fixed the issue.
Reset All Settings will not erase any content, apps, or change your account settings.