Apple are forcing owners of old iPhone 5 to update their devices to iOS 10.3.4 before November 3, 2019. Otherwiese the can't continue to use App Store, iCloud, E-Mail, Web and other services.
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Owners of such a device are seeing a popup windows shown below, notifying to update to iOS 10.3.4. The linked article from MSPU has more details.
Apple knows you don't want to update your old iPhone- so they've found a way to force you to. – https://t.co/rEHEnUrOcL pic.twitter.com/kBXDp0awUS
— MSPoweruser (@mspoweruser) October 27, 2019