More seriously, space is pretty cold, and will consume large amounts of radiated heat. The problem, of course, it that the amount you can radiate thermally at,

More seriously, space is pretty cold, and will consume large amounts of radiated heat. The problem, of course, it that the amount you can radiate thermally at, say, 150°C is pretty limited. According to the Stephan-Bolzmann equation, it's about 1800W for a perfect black body. For 5GW, that would take a square radiator 1.7km wide, always concealed from sunlight. Realistically, much larger as the temperature would drop as the coolant flows along.