Since they are both socket 775 CPU's, and there isn't anything else restricting you from installing the E5400, I would go ahead and make the switch.
Once you install it, if everything seems to be fine at first, go straight into BIOS and look to see if it's showing both cores. Or you could let Windows load and go into Task Manager and look for two graphs under CPU Usage. If there are two, and they are both running, all should be well. If there is still only one, you may need to do the re-install that patio suggested.
Odds are, you will probably need to update BIOS. And then even if all seems well, I would still do a fresh install of the OS. Just to avoid any possible complications.