> I can't install any apps from the "App Store" but it still does what I want most.

Apple has made this such a hassle... if you actually install an app on your new iPhone 10... you can go over to your "Purchased" on your iPhone 5 and install the version that runs on it (if it exists). However if you go on the iPhone 5 to the app store, they just say "so sorry, not supported" and it is the biggest slap you can give someone to remind them the product they paid for is not owned by them.