Try these steps and hopefully it will help you to solve your problem:
1. Make sure that you have removed the protective film from the screen.
2. It’s possible that your case is interfering with the noise cancelation feature. Try using the iPhone 5S with the case off.
3. Settings >>> General >>> Accessibility and turn Phone Noise Cancelation off to see if it makes a difference.
4. If the problem is with a specific app then make sure it has permission to use the microphone in Settings >>> Privacy >>> Microphone.
If your problem is still there, contact Apple customer service.