Should be fine. A 5850 can run on a quality 400w unit. It's not an award winner or anything though.
If you do decide to upgrade the PSU stick with Corsair, Seasonic, PC Power and Cooling, Antec, XFX, Silverstone or Enermax.
I am fairly sure OCZ owns PC Power and Cooling now and makes very good quality PSUs. There StealthXStream2 600w can really supply 700w.