Will this CPU work with my motherboard?

Hey guys, I'm looking to do a little upgrading to my computer, and I want to make sure I'm doing everything right. I currently have a Gigabyte GA-945GZM-S2 Rev. 3.9 motherboard with a Intel Pentium E2160. I am looking to upgrade that CPU. After a little research, I think I have narrowed it down to the E5000 Series, specifically the Intel Dual-Core E5400. I am wondering if this chip will work with my motherboard. I know the FSB will match up, but I'm worried about the chip tech. My current chip is a 65nm, and the one I would like is a 45nm. Can I still use the chip I want? Thanks for all the help!

P.S. If anyone can think of a better chip upgrade then the one I have, feel free to let me know.

I guess I should of added this in the OP, the website doesn't have any information about the entire E5000 series, it goes from E4000 to E6000.