Yeah the new spec sounds decent enough for what's likely needed here. I won't go into the finer details (and the i5 4570 vs i7 debate..lol) but your current machine would likely run the game with a few tweaks too. However, I'm guessing the age of the machine has some sway too... it only really needs more Ram and a Graphics card change for improvements to occur. But, like most machines, the m/b dictates how much Ram you can add, so it's likely not possible..?
But in terms of what you stated.. go for it. The Graphics Card issue is certainly worth looking a little harder at.. but if unsure, stick with something more commonly supported and throw the money at the Ram side. You'll only benefit with Ram if you're going to use it though..