It can help to take an approach of using an even number of splines.
This will not only help in avoiding 5 point patches but also 3 pointers... as well as chart a course for dividing larger sections as they get refined into (optimally) 4 point patches.
One of my favorite approaches... where the model will never leave Animation:Master... is to fully embrace 3 and 5 point patches and even leverage them in innovative ways.
For instance: intentionally creating a 5 point area so that it can be capped as a 5 point patch.
As a general rule, anywhere in a unibody mesh where there will be appendages (or orifices) there will be a requirement for a special patch (3 and 5 pointers being most used).
In the 'embrace the problem' category:
Another useful and old school approach is to hide the area in question.
For instance, we might hide 'eyes' behind a pair of glasses.
We might extend troublesome areas out of camera view... move them around to the side or scale... way... way down...
In the case of scaling it might be possible to leave a 5 point patch area completely open and it now be seen in the final rendering.
It might not be 'air tight' but... no one will know it isn't.
How about the 'grid based model with decals' approach?
Here a basic grid of 4 pointers in modified into a shape and details that would likely require 5 point patches... added via decals.
Then there is the 'fix it in post' approach where a troublesome areas is obscured, blended, blurred or otherwise tossed out.
For something like the current contest... which rightly places emphasis on using A:M for modeling and rendering... I'd say the embrace the 3 and 5 point patches approach would be the easiest approach rather than spend too much time trying to convert them into 4 point patches. There are some considerations of course with decaling and texturing and so those cases will need to be tested. If not seen in the final rendering though... you'll have more time to refine other elements of your contest entry.