Is this 780w G7 psu enough to run an ati 5850?

Yes it can. Both of your pcie 6 pin connectors run on a 12v rail at 18 amps. Which if you do Amps*volts - you get watts. Which it says it can put out a max of 216 watts. Which is enough power for a 5850.
 
A 5850 only draws around 130W at max (stock settings). Consider that the TDP for most CPUs is under 100W, and add in all the extra stuff (fans, mobo controllers, HDDs etc) you're only talking a usage of under 300W.

That said, they recommend 500W for safety factor.

Though, like Djentleman said, it depends more on what's available on the 12v rail since that's powering the important stuff :)

Anyway... yeah, 780W is good to power a pair of 5850s and then some.