From Lao Zi: The Book of Tao and Te (Chapter 42)
The Tao creates the One
From One come Two
From Two comes Three
From Three comes everything
NOTE: Translations of this text tend to vary a bit, so it is best to read in the original Mandarin Chinese (if possible).
There is also the idea of three representing heaven, earth and man. Finally, there is the use of Trigrams and Hexagrams to illustrate various possible life situations from the Chinese classic Book of Change.
RE: The number 5 in Chinese culture etc.
There is the concept of the five elements (fire, water, wood, earth and metal) from which all things are derived. Each of the five elements are tied to (or are used to represent) various other aspects of our world such as directions (south, north, east, center, west), body organs (heart, kidney, liver, stomach/spleen, lungs), colors, flavors, emotional states etc. This is an important part of traditional Chinese medicine and how they diagnose and treat illness. I believe the general idea of five elements also underlies much of the Chinese view of foods in terms of which foods/flavors go well together and their appropriateness for certain seasons, physical conditions etc.