Classic Firmware on 5g?

but it is possible for it to work?

With a bunch of hacking, I'd think. I doubt there's a hardware deficiency in the 5g that would prevent the firmware from functioning, providing somebody spent a bunch of time removing all the stuff Apple put in to stop you from doing that.
Actually, there are most likely hardware differences that would make it impossible to use a newer firmware on older ipods.

There are potentially a lot of hardware differences.

Even the 1G and 2G nanos last year were built on a completely different processor and chipset, and there were virtually no differences in those two models that were visible to the end user (the 2G had the "Search" feature, but that was really about it).

Now the new line comes along with a completely revamped interface. It's extremely unlikely that this is running on hardware that is even remotely similar when it comes right down to it. The incompatibility of the 5G games even speaks to potential graphics chip differences, and there are some obvious deficiencies in visual quality/effects even in those games that have been built-in (ie, Vortex) as compared to the 5G, implying a different graphics chip, in the very least.

It's extremely unlikely that the 5G is in any realistic way compatible with the new firmware. Of course, even if it was, the other posters are correct in that Apple has little motivation to provide it for the older models (there are still costs involved in doing this, and it's not worth any company's effort to expend money on a now-discontinued product).