Can I access the internet with cellular if I put a prepaid sim card into an iPhone 5?

I would like to get an iPhone, but I'm not really keen on committing to a three year plan, which would eventually add up to around $2000. My question is, if I get a factory unlocked iPhone straight from the Apple website, then buy a prepaid sim card, would I be able to access the internet using cellular?

You can only use a nano-sim or you would have to cut a micro-sim to fit.