1) if all of your internal settings are right (no settings for do not disturb, ringtones selected and turned on, etc) it might be a hard ware issue.
2) If you look at the left side of the iPhone 5, you will see an indentation with a thin switch, and the two round volume buttons. If that switch is pushed to the back of the phone, an orange line will appear. That puts your phone on silent. Flipped to the front of the phone, it just looks black, and the phone is not on silent. We just realized that this is what happened to ours; it must've gotten flipped while in pocket.
3) The kicker is that when the silent button is on, there is no indication on the screen. No icon with the little bell with a slash through it; nothing to tell you that the phone has actually been put on silent. Not the best innovation. You will see the little slashed bell pop up when you turn the phone onto silent, but then it disappears, giving no clue why your phone that can find answers to all questions in the googleverse won't ring when you get a call.
4) if none of this helps, hit the mac genius bar. They can fix just about anything.
