Is it the iphone or the sim card?

Hello!

My dad gave me his old Iphone 5 for my travels. We have used this phone before in the US, UK, and Nigeria as a travel phone. When I tried to use a Korean sim card, the phone read "no service". I have called virtually every US network (my dad bounced around from plan to plan alot) to figure out if it was somehow locked to carrier without us knowing. I was told many conflicting things until a Verizon rep said that it looks like the phone is unlocked based on their website. Since the phone has worked with other foreign sim cards before and it does not seem to be locked to a specific carrier, I wanted to know if it is a phone issue or a SIM card issue? Is there a hardware difference in Korea that I did not know about? They also have iphones here. I am very confused.