I'm running a r9 390 on a 550w OCZ ZS Series bronze psu just fine. With i5 4670 non k, 4x ram, a ton of fans, leds and 4 hard drives.
Given the 1080ti is listed for the same tdp, could I switch over to that without burning down the house? :')
But I think the 1080ti consumes 20w more than the 390 so my power draw would be 500-520 watts so I don't dare to upgrade to a 1080 ti xD
Your psu is 600w thats the minimum requirement listed by nvidia combined with an i7 on 3,4ghz. So you should be fine with your i5 I'd say, im here thinking about a psu upgrade because I'm 50w short of what I want.