Why don't IPhone 5's get the iOS 11 update?
Why don't the iPhone 5's get the ios11 upgrade
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Update the iOS software on your iPhone, iPad, or iPod touch - https://support.apple.com/HT204204 - Updating will only offer the highest available iOS version supported by that device. If it says no update is available and you need a higher version you will have to buy newer equipment.
As for why, presumably the hardware is too old to support features offered in iOS11.
Vintage and obsolete products - https://support.apple.com/HT201624