10-15 fps? Yikes. Even 20-30 is far too low for some.
Your frame rate is really low and your computer is having a hard time running FFXIV.
I've noticed that FFXIV is heavy on the GPU use but also heavy on the CPU as well. You can try dropping the settings down to try to eek out better frame rates (kill off AA, Occlusion Culling, etc.) to try to improve performance.
You can also attempt to overclock your CPU/GPU. I will say, if you go this route, you run a risk of damaging your machine. The chances are low, but you are pushing your equipment past it's designed parameters. If you OC and if you have a warranty, that warranty will be void.
I did some looking around for you and I couldn't really find any information on your specific model of computer, it looks like you CAN update your 620M drivers to trick it into thinking it's a 630M to push the core and memory clocks up. As for your i5, depends on the chipset, but it's definitely possible.
I want to reiterate the dangers of overclocking. If you don't do it right or know the values, you can will damage the hardware/software of your computer. If you overclock, you do so at your own risk:
http://forum.notebookreview.com/asus...-lounge-3.html
http://www.bit-tech.net/hardware/cpu...core-i5-2500k/
http://forum.notebookreview.com/asus...c-results.html
