Mac Pro 5,1 PCI GPU power 6/8 pin confusion
The 2 pins more in the in the 8 pin plug are 1x ground and Sense1. Sense1 is only to inform the card whether a 6 or 8 pin plug is plugged in.
I think the big difference in your usage is that 8-pin plugs are able to pull 150 W, where 6-pin plugs only provide 75 W at max.
As far as I see the Sapphire HD 7950 needs 80 W at idle.
So I see 3 Possibilities:

Buy a 6 to 8 Pin Cable and risk your power supply (amazon link) (worst idea)
Use the card with only 150 W max (75W from PCI Power Supply + 75 W directly of the mainboard)
Get another Power Supply