Will windows 8 work on a 5 year old computer?

Probably, but there's no way of being certain. On the M$ site there is an upgrade assistant you can download which should be able to find out if it works:

http://windows.microsoft.com/en-US/windows-8/upgrade-to-windows-8

Personally I dislike win 8 though and prefer Windows 7, I recommend you getting Windows 7 instead of 8.

MS make their software fatter and fatter to fit the speed and storage capabilities of the current PCs.

The processor speed should just be good enough - but would be on the low end of what would really work - so your machine will not exactly be fast.
The memory - again is more than the minimum spec but doubling it to 4 would be pretty cheap and would probably make the machine more usable.
The graphics card is the one thing that might stop it working.  Maybe google the model of the card and the words "windows 8" and see if anyone has already done it.

Here is the official listing :
http://windows.microsoft.com/en-US/windows-8/system-requirements

But if you really installed Win8 on a 1 GHz machine with 1 GB of ram and 16 GB free on the hard disk you would probably be able to open notepad and that would be about it :)

It should work (but no promises). It will be sluggish if you open more than 2 or 3 programs or files at once - and it will not be able to play any modern games.
One question - does it HAVE to be Win8 ? What about an earlier version of Windows that would suit your pc better ?  ...or... what about Linux.  Its free and brings old abandoned windows machines back to life years after MS gave up on them :)

Well, if my opinion help you here it is.

Windows 8 will work better than Windows 7.

I have used Windows 7 on two of my machines (work PC and a laptop)
Now I am using windows 8 on the same hardware and with same programs installed. From my personal experience I can tell that Windows 7 compared to Windows 8 looks like a resource hog and inferior predecessor.

Core 2 Duo Intel with 2GB of RAM will work just fine. Although considering how cheap RAM is these days I would recommend adding 2-4 more gigs so Windows can breathe better.

And one other thing, on most machines HDD is the bottleneck. If you would add an SSD to your configuration you would have a feeling that you have the new machine.

Regards,
Nik

Although as mentioned above, Win 8 should use less GPU power than Windows 7 uses (provided Aero is enabled), I've been able to get Windows 7 working with more Graphical cards properly, while Windows 8 will refuse to install any but the standard generic driver of m$, so you end up with low resolutions you can't setup properly, even with not too old cards. Other things you can run into problems with are sound cards and printers that may not be supported anymore.

Thanks a lot for the analysis and recommendations.  Your insight is very much appreciated.  I believe that you are right on with your recommendations!  A very thorough answer...the main reason that I am a member of Expert's Exchange is to find answers like this.  Keep up the good work.
capreol