It's a 5 year old computer. It's a workhorse not a powerhouse. The processor and graphics card were high-end at the time, but no more powerful than the high-end desktops. Processors and graphics cards have came a long way since then.
It also doesn't help that minecraft is quite demanding on your system. I know the vanilla server is now multithreaded (I think the modded servers like bukkit are still single threaded), I'm not so sure on the client. Do the right, or wrong, thing and it will bring todays system to their knees.