Yeah, that game is more CPU-demanding than GPU, so the CPU in the system would likely make more of a difference in performance.
As for the HD 5670 though, it's a card that launched for around USD $100 seven years ago, and there are certainly much faster cards available for under $100 now, like the current-generation RX 460, that should be around three times as fast, and can be found for as little as $70 after rebate. The 5670's performance is in a roughly similar range as the integrated graphics in the Intel Core processors from the last few years, although if that system has a 5670, I suspect it probably also has an older CPU with slower integrated graphics.