Camera flash / flashlight is not working, rear camera IS working

I recently replaced the battery on my iPhone 5S as the battery life was awful, and everything was working fine. Volume buttons up and down, flash, flashlight, both cameras were all good. I went to take a picture last night and now the flash is not working. I tried turning the flashlight off and on, doing a home & power button reset, and a system restore - everything that you can find online to try, I have tried.

Would replacing the camera itself fix the LED problem? I see from other posts that the camera assembly is different in the 5S from the 5 and 5C, the LED light looks to be a separate piece from the camera now. I haven't seen the LED part for sale anywhere.

Any ideas or how-to-fix answers would be greatly appreciated! And in simple terms please - I am a little tech savvy but need guidance. Thank you!