Will a Verizon iPhone 5 work in South Korea?

I'm attending university in Seoul for 5 months and I'm deciding if I should buy a new iPhone in New York before I go. Right now I have an iPhone 4 without a sim card slot, so I either have to buy a phone here or buy one in Seoul. I think it's really important to have wifi at the very least, but really would prefer being able to use data (3G or LTE) when I'm in Korea. Does anyone know if the iPhone will definitely work? Because otherwise I'm considering just getting a free phone with a sim card, or just buying a phone in Seoul.