Is my existing PSU good enough for new build?

I would think so .... my experience of late is limited to the Antec Signature and Corsair HX series where if it says 600 watts, you can be sure it can deliver 600 watts.

I ran your system over at http://www.antec.outervision.com/PSUEngine

and got 466 watts w/ 85% TDP, 90% load and 25% capacitor aging. Had to use a 5870 as the pick-list didn't include a 5850 and I was too lazy to look it up so this is high

We're note exactly done yet and you do want some headroom between where you are routinely operating and what your peak rating is. If designing a new system, I'd look for 466 x 1.5 or 700 watts ..... for long term stability and efficiency.

In that case I'd probably select select a 650 considering the 5850/5870 thing but for your situation 600/466 (less actually) is still about 1.3 which is certainly within the safe range even w/ a 5870.

The official ATI recommendation for a pc system with single 5850 video card is a 500 watt power supply.

The general rule of thumb is a high quality 500 to 550 watt power supply with sufficient current (amps) on the 12 volt rail(s) can easily power a system with any single video card made.

You should be okay for now. However, if you add a second 5850 then you will have to upgrade the psu.