"The Radeon HD 5670 is the most powerful card you can buy that doesn't require an auxiliary PCIe power cable"
If you look at the links I supplied, it's rated at just 61W under FULL LOAD. The PCIe slot can supply up to 75W, that's why no 6-pin plug is required. And if you do the math, 61W / 12V = 5.08A. But since the PCIe slot gets a portion of it's power from the +3.3V rail, the card will be pulling less than 5.0A from the +12v rail while under FULL LOAD.
You have 19A on the +12v rail & a weak CPU that's rated at 62W. The CPU get's 100% of it's power from the +12v, so do the math again: 62W / 12V = 5.17A. Now add them up: 5.17A + 5.0A = 10.17A. You have about 9.0A leftover for the HDD, optical drive & fans, which is more than enough.
If you think 1.0A is gonna make a difference, then go with the inferior GT 430. Or I have a really wild idea - how about upgrading the video card AND the power supply? WOW!