(top) In general, phyllotaxis is the result of a process of closepacking of little humps before organ differentiation. None of the precisely ordened primordia in a very young sunflower looks like the little flower into it will soon be transformed (photo by Pieters, 1998 - diameter~1mm).
(bottom) In the flower left, the number 5 (and rings of 2x5=10 near the center) is a direct consequence of closepacking. Here, phyllotaxis and differentiation were two parallel processes, resulting in rings with similar parts. This phenomenon is called canalization. Compare the three examples.