Verizon iPhone 5 Internet won't connect on LTE

When I turn on cellular data and LTE on my Verizon iPhone 5, half the time it won't connect to the internet. Signal strength seems to have no effect since it has worked fine before with 2 or 3 bars, yet sometimes I have 5 bars and it won't work connect. I've tried turning data off and on again, as well as turning airplane mode on and back off. I'm not sure if it's just the region I'm driving through at the time but I don't think it is. Is this a problem with my phone or with the carrier and cell towers?