How do I set my iphone 5 to network and not just wifi connectivity? Any time I leave my house, I have no internet connection...

Check Settings>General>Cullular Data, make sure this is set to On. If it is and you still can't get a cullular internet connection contact your carrier and check to be sure your data plan is properly provisioned.

I have the same issue (can't connect to Internet as no data subscription provided) & contacted my carrier (Telstra, Australia). We tried to change the cellular network APN in settings/general/cellular data, but that didn't work. Apparently they need to change a code on my account in one of there systems, which will take 24 - 48 hrs. If you haven't already, contact your carrier as they may need to make an adjustment to the settings at their end.