Yes, you can run GTA V in 1080p.
Equipment details: Asrock z77 Extreme4 with Intel i5 2500k, 3.3GHz, Sapphire 5670, 1GB DDR5 memory, 400W power supply, DDR3 4GB RAM, Barracuda 500GB hard drive.
It's possible you're only achieving around 50-60 frames per second, especially if you've reduced settings.