Only 770 I know that will fit is the msi 770 twin frozr. Most other 770s will fit but requires modding the case. I have modded the case and have a msi 280x twin frozr in a sg06 with an S model i5 as it is slightly too long for the sg05. Temps are fine with the gpu going up to 74c and cpu 60c.
As for power you should, even be ok to do some intel cpu overclocking.
Unfortunately, most 280/X cannot fit in sg05 without modding so best option would be 770 or 760.