If you have managed to hold your iPhone 5 from 2012 so far, you should probably update it before November 3.
You have to update to iOS 10.3.4 for important functions, including the App Store, iCloud, email and web browsing to work, according to Apple. If you are not sure which version you are using, Apple has a support page about the problem, which also explains how you can check which version you are using.
Your phone needs the update due to the GPS time rollover issue. In short, GPS devices measure the date and time using a weekly counter can only count until week 1.024, after which the counter is reset to zero. Because GPS requires accurate time data to function, the reset can also disrupt location data. Date resets are a recurring problem for technology, probably best known in the Millennium / Y2K bug.
Have been newer devices designed to adapt to the rollover, according to Ars Technica, and it can only be your GPS accuracy that is affected by the bug if you are affected at all. Apple says the iPhone 4S, the first generation iPad mini, iPad 2 and the fourth and third generation iPad need an update to make their GPS work accurately, although other functions must continue to work if you forget to update. Verizon said the GPS accuracy can be affected on any device built between 2006 and 2016, and published a list of affected devices here.
Fortunately, there is a simple solution for most devices: just update.
You can update your phone wirelessly or via your computer before November 3rd. Here are Apple's instructions on how to do that. However, if you did not install the update before November 3, Apple says that wireless updates and iCloud backup will also stop working because the GPS problem affects iCloud. If that happens, you must back up your phone and restore it using a computer. Here is another guide on how to do that.
Clocks have stopped Apple products earlier. A bug caused iPhones to crash several times as soon as the clock struck December 2, 2017 at 12:15 PM. Last year, summer time confused Apple Watches by securing them in a crash and restart loop.
Apple says the GPS rollover will not affect their devices until November 3 at 12:00 AM UTC on November 3, that's 8:00 PM ET on November 2. But don't wait until then – update your phone now!