Five is the number a tradition reaches for when it wants a complete set that includes the observer, and it very often arrives by adding a centre to a four.
Chinese cosmology is the clearest case. The five phases, wood, fire, earth, metal and water, govern a scheme in which colours, directions, organs, tastes, seasons and notes are all counted in fives, and earth sits at the centre of the four quarters rather than beside them. Indian tradition counts five gross elements, adding space to earth, water, fire and air, and builds the five sheaths of the person and the five vital breaths on the same footing. Aristotle added a fifth substance to the Greek four for the heavens, and the Latin word for it, quintessence, has outlived the physics entirely.
Where five appears without a four underneath it, it is usually because a tradition has counted its own obligations. Islam names five pillars and prescribes five daily prayers. Sikhism gives the five articles of faith worn on the body, and the five beloved ones of its founding narrative. The Torah is five books, which is why Greek-speaking Jews called it the Pentateuch.
Christian devotion counts the five wounds, a late medieval focus that produced its own prayers and iconography.
The Greek arithmologists, characteristically, took a structural view. Five is the marriage number, the first sum of the first even and the first odd, since one was not counted among the numbers at all.