So, then I would say that rules out the display. If you're power supply is adequate, then you should have no issues with the card. There are quite a number of reports on the 5000 series mentioning artifacts and lines but this is the first I've read of the display flickering. Make sure the refresh rate is maxed out for the monitor and if that doesn't fix it I'd say RMA the card. I know it's a bit of a hassle to go through but that's honestly what I'd do if I were in the situation.
