Try a visit to http://www.spinwave.com/crunchers.html,
browse to find your
jpg or gif, and see what they can offer in terms of reducing colour depth.
I don't think you're going to get down to 5k, though.
Cut the white space by all means, but neither jpg nor gif takes much space
for unchanging colour areas. I suspect it's your shadow that is keeping the
size of the file up - see how the main image stays much the same as the
colours reduce, but the shadow suffers.
It's not a big file really, and if it's the only significant graphic on an
explanatory page you should have no problem. Take it down to 12-14k if you
like, but you should be OK for most collie enthusiasts.