You would be surprised to see how far 4GB of RAM will take you. It's totally adequate for just about every modern game.
Unless you're willing to pay a lot of money for a new graphics card, you're not going to get a big upgrade over what you have now. Speaking of which, what sort of budget did you have in mind for this new stuff? Both the Radeon HD 7870 and the GeForce GTX 660 Ti would beat your 5850 by a nice margin at the cost of $250. If you really want a jump in performance beyond that, it'll be to the tune of $300+.
That CPU was probably a great and inexpensive choice for your computer back in 2010 when you built this thing. But today, it's getting dated. I'm not saying you'll ABSOLUTELY need to upgrade that too, but it might come back to bite you later.