To be more specific, I have a AMD Anthlon 64 x2 5600+ 2.90 GHz and my friend is going to give me his tower which has AMD Athlon(tm) II X4 640 Processor. I was wondering if I can add them together on the same motherboard if that makes any sense
No you won't be able to. There are dual and even quad socket motherboards out there to allow for multiple CPUs, but they are aimed exclusively at the server market. There are no consumer desktop motherboards that support more than 1 CPU. Even if you did have such a motherboard, consumer CPUs do not support running with another CPU. When running multiple CPUs, they are also identical chips, you have two different chips from two different generations. It just isn't going to happen.
The Athlon II will be a good deal faster than your old Athlon 64, so just be happy with the performance boost. If you want more performance, consider upgrading to a Phenom II or one of the FX x3xx chips if the motherboard supports them.