[saspinski (OP)]

Of couse there are also examples of 3-fold, but 5 seems to me the most common type. I wonder if it is related to some orbital angle in relevant molecules. But searching the web, I found typical angles of 109.5, 120 or 180 for organic molecules. Nothing that can explain 5-fold simmetry. 

[Janus]

The number of petals on many flowers follow the Fibonacci series: 1,2,3,5,8,13,21,34,58...
This has to do with the most efficient way for the flower to grow out from the center.  In many cases the center of the flower consists of seed that grow outward from the center.  The way to make the best use of the space is to grow in a pattern called a Fibonacci spiral, like this.
https://www.mathsisfun.com/numbers/images/phi-flower.jpg
This results in the out-most layer consisting of a number on the Fibonacci series, and this is were the petals originate. It is a geometry issue, but one sealing with how to maximize use of space, and not molecular bonds.

[Bored chemist]

It's true that a lot of daisies
https://en.wikipedia.org/wiki/Asteraceae
have fibonacci series embedded in the flowers but I think the OP is referring to the roses
https://en.wikipedia.org/wiki/Rosids
which usually have 5 fold symmetry.
It's an interesting question and I have no real idea what the answer is.