This is not how we want your iPhone 5S working. Let's see if we can get it going for you. Just need a little more info from you: How long has your device been like this? Are you able to hear anything when you play any music or videos without putting on speaker? Is there any physical damage to the device? (cracks, water damage, corrosion)
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no water damaged, no physical damaged. it just stopped working. i can still hear music from the speaker. the phone is not even a year old. bought it last november 2014.
I've read on here that some folks have had similar issues. Try doing a hard reset...its been reported here on the forum that doing so has restored functionality for some. If you're still having a problem after that...I'd take it to the Apple Store. Since you just purchased it 11/2014 then you're still covered under Apple's warranty.
the software on your phone may be off, try connecting the phone to iTunes to perform a rest and ensure that the software is up to date