Did you try calibrating by choosing a floor climb or GPS activity and waiting 30 seconds before starting? I also presume the Fenix has a port hole for the barometer chip on the watch's underside which can get dirty over time and can be cleaned by running it under water.
I don't know how to do it in a Fenix 5S but there's a way to test if the barometer chip is functioning which someone here probably knows. Otherwise contact Garmin support for instructions.
Also, it probably is a good idea to post this in the Fenix rather than in the android sub-forum. Others with your device are more likely to help you there.
