Lots of people have liked the 5-pointed star; I am not sure what you are trying to get at.
I assume you have something more in mind.
Yes, the number 5 is part of what's important, and the geometry involved is also something to consider. Here are four of the flags that were proposed and used in various capacities by the League of Nations over the years, none `officially,' yet some being flown for as long as 2 years:

The significance of these last three flags, all designed "to symbolize five continents and five races" ... can be understood as a natural progression of grasping something of the Unity which is symbolized by the earlier flag, with a dark background, the unfolded world in oval shape, surrounded by as many stars as the League had member states.
The final flag, with its stars within stars within stars, emphasizes yet other esoteric principles and
perspectives on the scale of being (aspects of existence we can scarcely fathom) which might be imagined as extending into unbounded Infinity, yet which we must accept for the moment as limited from our vision by the *sides* of the pentagon.
One really does not know how ugly a cynical, pessimistic expression and choice of self-limitation appears from the realm of Beauty ... until one stares it face-on in the mirror, and feels the repulsion which separativeness, fear, demonization, and all of the more petty, `lower vices' cause - in the heart and mind of the spiritual soul, or SELF.
It is these collected obstacles to individual progress and real spiritual effectiveness, or their larger aggregations and
phantom self, which prey upon the workers in the field, sapping the strength of well-meaning souls and their group endeavors, which have delayed the accomplishing of the goals set forth by the League of Nations, the United Nations and even that future expression of the same entity - as yet unnamed, as yet un-incarnate.
As above, so below ... aren't these the cause of the holdup to our
own progress toward harmony, cooperation and enlightenment? As with men, so with nations.
Pythagoras taught a thoroughly Spiritual Philosophy. His students are scattered across the Globe; the Wisdom of Krotona lives on.
Pythagoras was thoroughly familiar with the Vedic teachings regarding man's evolution. This was reflected in his own teachings on geometry. Maybe you know about the Tetraktys, bob x?