Will iPhone 5s work after November 3

The iPhone 5c and 5s are not affected by this issue, only the iPhone 5, NOT the 5c or 5s.

If you have a 5s you do not need to worry.

If you have a 5 (non Touch ID), you need to upgrade to 10.3.4 in order to maintain functionality.

Please note only your GPS will not work

Update your iPhone or iPad software to avoid issues with location

Starting just before 12:00 a.m. UTC on November 3, 2019,* some iPhone and iPad models introduced in 2012 and earlier will require an iOS update to maintain accurate GPS location. This is due to the GPS time rollover issue that began affecting GPS-enabled products from other manufacturers on April 6, 2019. Affected Apple devices are not impacted until just before 12:00 a.m. UTC on November 3, 2019.

Of course it will work. My iPhone 3GS and 4S still works fine.

You are welcome.