Q: Does anyone have problems with iPhone 5 getting hot?

Does it get hot to the point where it might burn you? IF SO- I'd either take it into an Apple Store or go ahead & call Apple Care. If you JUST purchased it, you should still be within your complimentary 90days of phone Support.

I would try restoring it to see if it still happens. If its getting too hot for you though, stop using it immediately and go to the Apple Store or call them at 1.800.275.2273

That depends on how hot it gets. With a weak cellular signal the phone must increase its output power significantly (10 times normal or more), and as a result the phone will get warm. It has a thermal overload protector, so it should never get dangerously (to the phone) hot. It should never get so hot you can't hold it.

FaceTime uses up a lot of battery power, that would cause the phone to get hot. The device does and is expected to get hot when the battery is in use. Be worried if you get the alert for the temperature.

Do you have any kind of resource that says this?

http://support.apple.com/kb/HT2101?viewlocale=en_US

It is normal for it to get warm when it's being used, especially if it is hot outside. It can even get uncomfortably warm. As long as it is not causing you physical harm (as in giving you burns) or displaying a temperature warning, then it's normal behavior. It's like taking your laptop outside and using it. Except the laptop will probably burn you.