An astronomical pattern that is real
Of all the claims made about five, the link to Venus is unusual because it starts from something that can be checked. Seen from Earth, Venus repeats a cycle that fits neatly into five episodes in eight years. Astrologers and occult writers later built symbolism on top of this, and that symbolism is a matter of belief. The astronomy, though, is plain observation and arithmetic.
The numbers
Venus passes between Earth and the Sun, or behind the Sun, at regular intervals. The time from one meeting of this kind to the next, as seen from Earth, is called the synodic period, and for Venus it is about 584 days. Eight years of 365 days come to 2,920 days, and five times 584 is also 2,920. The match is not perfect, since a year is a little over 365 days and the synodic period is close to, not exactly, 584 days, but the two totals differ by only a few days. So after about eight years, Venus and the Sun are again in nearly the same arrangement against the sky.
Venus also circles the Sun in about 225 days, and thirteen of those orbits take close to eight years. The result is a ratio of thirteen Venus years to eight Earth years, and five meetings between them. This kind of near-commensurability is a general feature of orbits, comparable in spirit to the nineteen-year Metonic cycle that links solar years and lunar months.
Why it draws a star
The pentagram comes from where those meetings occur. When Venus passes between Earth and the Sun, it does so at a particular point on the zodiac. After 584 days the Sun has moved on by about 1.6 circuits of the sky, so the next meeting takes place about 144 degrees back along the zodiac from the last one. (The Sun covers about 576 degrees in 584 days, which is one full turn plus roughly 216 degrees; stepping 216 degrees forward is the same as stepping 144 degrees back.)
A step of 144 degrees is two-fifths of a full circle. Marking five points around a circle and joining each to the point two places along gives a five-pointed star. After five meetings the pattern closes, which is the same eight-year cycle described above. Plotted on a chart, the positions of Venus’s meetings with the Sun therefore outline a pentagram, or, if the positions are marked with petals, a five-petalled flower shape. This is why the pattern is sometimes called the “Venus rose” in popular writing, though that name is modern.
What older observers recorded
Observers in several ancient cultures tracked Venus carefully. Babylonian astronomical records followed its risings and settings, and the Maya kept a Venus table in the Dresden Codex that is based on the 584-day cycle and on five cycles making eight years. These records show interest in the cycle’s repeats. They do not, as far as the sources show, describe a pentagram, and they were part of wider calendar systems, in the Maya case alongside the Long Count, rather than of numerology as it is now understood. The idea of Venus tracing a star appears to be a later way of describing the same data.
Mesopotamian art often shows a star for the goddess Ishtar, whose planet was Venus, but that star is usually drawn with eight points, not five, so the sign cannot be used as evidence for a five-pointed link.
The pentagram as a symbol
The five-pointed star has a long history as a symbol in its own right. Later Greek writers associated it with the Pythagoreans and said it served as a sign of recognition among them. This is reported at a distance, so treat it as tradition. In the Middle Ages the pentangle was a Christian sign, famously carried on Sir Gawain’s shield in the fourteenth-century poem, with the points standing for sets of five virtues and wounds. In the Renaissance, writers on magic placed a human figure inside it, with the five points matching the head and four limbs.
Geometrically, the pentagram is full of the golden ratio: each pair of crossing lines divides each other in that proportion. This feature is thought to have been known to Greek geometers working on the pentagon, and it may be a reason that the star acquired a reputation for hidden order.
What astrology made of it
Some modern occult and astrological writers connect the Venus pentagram with love, beauty and harmony, since Venus is the planet of those themes in Western astrology. They then add five to numerology as a Venusian or Mercurial number, depending on which author is read, and the two sources disagree. These are symbolic readings, and there is no demonstrated link between the planet’s cycle and the character or fortunes of anyone.
It is worth contrasting the Venus pattern with the other star in this area of symbolism, the six-pointed shape described under hexagon and hexagram. Six-pointed forms come from a different geometry and a different tradition.
What can be said
The accurate summary is short. Five synodic periods of Venus are close to eight years, successive meetings are about 144 degrees apart, and joining them gives a five-pointed star. Cultures watched and recorded the cycle, and later writers connected the star to Venus and to five. Everything beyond that, the claims about meaning and influence, belongs to the history of belief.