Ati HD 5850 1gb and my PSU?

You are getting a little close to it's max. Sure a 650w can run a i7 with two 9800gt in sli but a 5850 with a 600w maybe. Go ahead and get the card and if the volts on the 12v rail dip below 11.4v get a new psu. If the psu makes all sorts of strange sounds while in use get a new on.
 
Google doesn't give us the max combined wattage on the 12V rails (should be on the label), so there's no way to tell whether it'll work or not.

A 450W Corsair PSU will power your rig with a 5850, but this Thermaltake 600W might not, it all depends on the max combined wattage on the 12V rails.
 


It uses 40W more and considering the fact you should always stay under 80% of the max combined 12V rails load, you need 50W more on the 12V rails.
 


It depends on the max combined wattage of those 12V rails, this could be less that 2X19A*12V = 456, it also has to have two PCI-E connectors.
 
Use this http://extreme.outervision.com/psucalculatorlite.jsp. It will give a general number that would need to run the rig. If yous is above the numbers it should work. But if it is borderline, I would be careful. Worst comes to worst, you buy a larger power supply.
 


It's fairly easy actually:

[130W (CPU) + 15W (hard drive and fans) + 20W (DVD-RW) + 150W (HD 5850) or 190W (HD 5870)]*(10/8) = 400W (34amps) or 450W (38 amps) combined max wattage of the 12V rails, you also need two PCI-E connectors.