I have it from the horse's mouth that a 7'200 NM trip was made with all necessary reserves and 5 people on board with a G650, without the ER STC.
If you fly the speeds as published, Gulfstreams tend to overperform the published figures. Be careful to consider ALL factors of your flight (Load, Temperatures en route, available flight levels, etc...) before committing to a figure...
I have done 6490 air miles myself with an older G5, 4 people on board.. The reason we had almost 3'000lbs on board at landing was that we had consistent ISA -15 over the whole route, were able to get some non-standard intermediate levels, and flew consistent LRC. Had we done optimum climb and descent profiles for fuel we could have saved another 200-300 lbs.