All iPhone 5's are 4G or LTE. At times, you may not have a 4G or LTE signal so it will say 3G. Sometimes, if you don't have 3G or 4G, you will have a little circle that barely gives you internet acess. If you don't have the worlds LTE or 4G on the upper right of your iPhone then something is wrong. I would call your cell phone provider first and if they don't have any tips then contact Apple. It could be that you are in a remote location without 4G or LTE service or it could be a problem with your SIM card. But either way, it is nothing that anyone on Yahoo Answers can do.
Actually though, go to Settings, General, Cellular, and see if the slider for "Enable LTE" is on. That could be your problem actually. But if it is on, do what I said above.