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The answer is yes, you can use a Samsung Galaxy S5, S6, or iPhone 6, or other unlocked LTE phones, in South Korea. This is better than the old days when Korea's adherence to the CDMA standard made it unlikely for outsiders to show up with a usable phone.
I bought a SIM card from one of the several shops at Incheon International Airport (ICN) near Seoul. It cost about US $25 for 1 GB of data, and was active as soon as I plugged it in. So you do not need a service that lets you reserve a SIM card in advance, despite those services claiming you do need them or you'll have to wait days to get activated. Maybe that was true in the past, but it isn't now. The SIM card sold in the airport was billed as valid for 15 days only, but in reality it worked until the 1 GB of data ran out (I used it for about 19 days). Unfortunately they said it is not rechargeable.