It is hard finding answers to this question, which also interests me a lot. The most satisfying answer I have found is detailed in this paper http://www.ijpam.eu/contents/2012-78-3/6/6.pdf.
From the abstract : "This article examines why many flowers are five-petaled through the use of a five-petal model that draws insight from the location of cell clusters at a shoot apex, rather than from concepts such as the Fibonacci sequence or the Golden ratio which have been referred to in the past. The conclusions drawn are that flowers are most likely to be five-petaled, followed by six-petaled flowers, and that four petals are unstable and almost no flower can be seven-petaled."
As for the alternative theory alluded to at the end of this abstract, you may want to check out the work of mathematician Michael S. Schneider (Master's Degree in Mathematics Education from University of Florida). His answer revolves around this idea where, much like what Plato proposed, geometry is seen as the fundamental building block of the universe and where geometric patterns (therefore numbers) are given different meanings based on observational data. In this theory the number five is seen as the "flag of life" if you will. Look-up an image of a DNA strand viewed along axis, I find it interesting that it's mostly in series of five.
That being said, the article I linked certaintly contains a more satisfying answer to your question.
Hope this helped.