You don't mention what OS you are using. I have 3 1070s undervoltaged to 85% TDP and am pulling 512 watts at the wall using a Kilowatt meter. You don't specify if you are undervolting or not. At least with my current settings there is no way I could run 6 GPUs on a 1000 watt P/S.
With 5 GPUs in, check the power draw at the wall and see how close you are to 1000 watts. If you don't have enough power you can either go to a larger single power supply (1300 watt) or get two 750 watt and get the connector that turns them both on at the same time.
Also you don't mention what happens when you put the 6th GPU in, does the system not boot or does the system turn off when you start the miner?
the psu runs fine with 5, 6 shouldnt be a problem. i use windows 10.
edit maybe upgrade my psu or get another one i think.