While a new iPhone is an option, you could simply erase and restore your 5s to its factory settings, which I think would restore using the latest iOS - 10.3.2. ...You'll lose all your custom settings; so, it will be like starting up a new iPhone and, you'll have to again reenter all. But, it may revive your 5s.
At any rate, I've tried just about everything that I can think of, and everything Apple support can think of, with no success (including a full restore to new).
Emphasis added