One of the key insights into the nature of cooking is that all cuisines respect the role of limited resources.
One of these limited resources is the number of ingredients that can plausibly be obtained. Traditionally, this has always been limited by the seasons.
If you have limited resources then you might think that you'd have a limited number of dishes. But you'd be wrong!
Humans recognized quite early on that we are easily bored. We crave novelty and variety. The same ol', same ol' was as dreary a millenium ago as it is today.
Traditonally, most cooking was done by women, and women were responsible for coming up with "inventive dishes" each day (to stave off that afore-stated boredom.) They were forced, at the metaphorical gunpoint, to get creative about it.
Lo and behold, the Japanese discovered the combinatorial game. Have a vast amount of ingredients at hand but assemble a dish with just a few and rotate them daily. In fact, outsource a few so that you only need to assemble the rest (the Ricardo-principle applied to cuisine.)
Needless to say, one can't do this with a hard-core mathematician's approach since that would lead to entirely unappetizing dishes so a few rules are imposed on top of that to maintain visual appeal, textural interest and nutritional completeness.
If you understand this then the rules of the so called washoku become entirely obvious.
The rules of go shiki (five colors), go mi (five tastes), go hou (five methods), go kan (five senses) are nothing more than a rulebook to ensure complexity - visual, textural, and nutritional.
The traditional dish is not made with five ingredients. It's closer to between seven and nine in practice. That would imply that you scale as where n is the number of starting ingredients (and n is very large to start with.) However, the above rules cut down the number of possibilities.
In any case, you are still left with a vast set to play with. Enough to stave off boredom before the seasons change which will alleviate the boredom anyway, and by the time next year rolls around nobody will remember that you played the same game last year!