This is a pretty obvious point, but if you haven't already switched to an open air case, this is the best cooling solution. I'm not sure how much aftermarket coolers would really help inside a case.
you'd be surprised
Max stable clocks for mining used
Reference 5870 with stock heatsink + fan @ 1015/330 1.187v 100% fan = 85c @ 24c ambient (increase of 61c)
Reference 5870 with Zalman VF3000A @ 1045/330 1.187v, assuming 100% fan (does not directly plug into card; it instead uses a "fanmate" which allows manual fan speed outside the control of your OS, or you plug it into your motherboard's fan headers) = 57c @ 24c ambient (increase of 33c)
This is inside a "closed" case with some fans screwed onto the side.
With a 5830, I imagine you can expect similar numbers. Maybe from 50c increase from ambient to an increase of 30c. There is a catch though. If your card is nonreference, it's possible the VF3000A will not fit. AFAIK, though, the 5830 extreme comes with it's own VRM heatsink, and the HSF assembly is just for the GPU core and clear of any other components, so a VF3000A -should- fit, granted the mounting holes are the same as a reference. You would just use the VRM heatsink that comes stock, and use the ramsinks as a bonus.
Also be aware the VF3000A blocks not one but TWO adjacent slots, so you will need to plan accordingly. The VF3000A runs about $50 USD, but you might be able to get lucky and find one for about $40.