BF3/SKyrim, also getting fps drops in sc2 during big battles

First off thanks for taking the time to read my post. I did not know where exactly to post this as my question overlaps with a few topics. Firstly, I was wondering what kind of upgrades I would need to make to my current system to be able to play BF3 and Skyrim on high settings. I realize this question has been asked before, but I'd rather ask on this forum than risk getting jipped by a saleman at a store. Here are my current specs:

OS: Windows 7 Home Premium 64-bit
Processor: AMD Phenom(tm) II X4 955 Processor (4 CPUs), ~3.2GHz
Memory: 4096MB RAM
ATI Radeon HD 5700 Series (I believe its a sapphire 5770 to be exact not sure though.)
Resolution: 1680x1050

Also, I am getting drops in fps in sc2 and CoH when a activity gets higher, meaning more units/battles. However, it does so despite what graphics level I am on.

thanks and any help is appreciated.