Caller can't hear me iPhone 5s 16GB Gold
When I make or receive a call, person on other end can't hear me unless I put phone on speaker?
I would start by taking a sewing needle and some air duster and try cleaning out the set of 10 small holes next to the audio jack. If this doesn't work. I would recommend opening the phone and checking to see if the dock flex connector is properly seated. It is located towards the bottom right side of the battery, above the battery connector. Use an iPhone 5s disassembly guide here on ifixit. No need to disconnect the LCD or anything. If you find it is connected and is still not working, you are most likely gonna need a dock flex cable. It's a very simple installation. I'll link the part you need and the guide for it.
Josh's answer is excellent; there's an even simpler failure that sometimes happens. Try putting in headphones and pulling them out again. Sometimes dust etc. gets wedged in the contacts of the headphone jack and causes the phone not to go back into the 'handset mode.' Putting headphones in a time or two will sometimes fix this, and it's a useful diagnostic in any case.