Welcome to iMore! A couple of ideas:
1. As @MrMike6by9 stated, check for something blocking the audio port on your 5s. If you have some compressed air give the port a quick blast.
2. It could also be the audio cable so try using another cable if you haven't already.
3. Reset your device by holding the power button and home button down simultaneously until you see the Apple boot logo.
4. Do you hear music playing before the audio cable is plugged in? Make sure your iPhone isn't on silent mode using the switch on the side of the device, and make sure that the volume is turned up. The Music app will play music regardless of whether or not the iPhone is on silent but some music apps won't.