Sorry buddy, but that's not the case.
http://img121.imageshack.us/img121/5853/96558056.png
According to this the 480 only consumes 16 more watts than the 5970. Assuming you haven't taken a physics course yet, a Watt is a Joule per Second. Keep in mind that a Joule is a very small amount of energy, which is why energy is often recorded in terms of KiloWatt-hours (which is essentially 1000x3600 Joules). So putting that into perspective, 16 watts really won't make a difference, even over the course of a year's use.
However, compared to the 4870 (which it is only slightly more powerful in many cases), the 480 consumes 150 more watts. Multiply that by 3600 seconds in an hour, and an average of 2 hours a day, times 7 days a week, and finally 365 days in a year, and then yes, the difference would be quite large. Would those savings much up the cost of another 4870? I couldn't tell you, I have no clue what electricity rates are in most places.