The middle of the sign
Across the years 1930 to 2035, the noon Sun on 5 January falls between about 14.0 and 15.4 degrees of Capricorn. The midpoint of the sign is fifteen degrees exactly, so this birthday sits within roughly a degree of the centre in every year of that span.
The tradition calls the fifteenth degree of a sign its heart, and treats a planet there as expressing the sign without dilution from either neighbour. Whether that carries weight is a matter of interpretation, but the position itself is a plain fact about where the Sun is.
It also means this is about as far from an ambiguous answer as a birthday can be. The nearest sign boundary in either direction is roughly a fortnight away, and the nearest decan boundary is five degrees off, so no year, hour or time zone puts anything about the position in question.
Why the position hardly shifts
The Sun reaches any given longitude about six hours later each year than the last, because the tropical year exceeds 365 days by close to a quarter of a day. Every fourth year the extra February date resets the accumulation almost exactly.
The visible effect is a small sawtooth. Over more than a century, this date stays inside a band under a degree and a half wide rather than drifting steadily in one direction. Any birthday in the calendar behaves the same way, which is why the sign attached to a date is stable even though the exact ingress moments are not.
The century rules refine this further. A leap day is skipped in 1900 and 2100 but kept in 2000, which keeps the average calendar year within half a minute of the tropical one. That is why a date from the 1930s and a date from the 2030s give almost the same answer.
The decan and its two rulers
Fourteen or fifteen degrees is the middle of the second decan of Capricorn, the band from ten to twenty. In the Chaldean order of the thirty six faces that band belongs to Mars. In the triplicity scheme it belongs to Taurus, and so to Venus.
Both are traditional and both are quoted online, usually without naming the scheme, so readers regularly encounter contradictory answers for their own birthday. On this date the decan itself is not in doubt at any hour of any year, only the choice of scheme.
The reading given to Capricorn is Saturnian: patience, structure, a long view of effort. The decan adds either a Martial sharpness or a Venusian steadiness depending on which ruler you follow. That is inherited interpretation, and it is offered here as interpretation rather than as fact.
What the date still leaves open
Nothing above says anything about the Moon or the rising sign. The Moon moves about thirteen degrees a day and so may be in either of two signs on 5 January, decided by the hour. The Ascendant depends on the hour and the latitude together and can be any of the twelve.
The widget above uses your own year and birthplace to compute your solar degree exactly, rather than the noon figures quoted here, and reports the distance from your Sun to the nearest sign boundary.
What the widget cannot do is supply the hour. If your birth record has a time on it, that single number does more to individuate a chart than everything on this page put together, because it fixes the Moon and produces an Ascendant.
Questions people ask about this
What sign is 5 January?
Capricorn, in every year of the modern calendar. The date sits near the middle of the sign, far from both the Sagittarius and the Aquarius boundaries.
What is the fifteenth degree of a sign?
Its exact midpoint. The tradition treats a planet there as sitting in the heart of the sign, uninfluenced by the signs on either side. It is a positional fact given a symbolic reading.
What degree is the Sun on 5 January?
Roughly 14.0 to 15.4 degrees of Capricorn at noon over 1930 to 2035. Your own value depends on your year, your birth hour and your time zone.
Which decan is a 5 January birthday?
The second decan of Capricorn. At around fifteen degrees the Sun sits in the middle of that band, comfortably clear of both decan boundaries.
Does being in the middle of a sign matter?
The tradition says it strengthens the sign's expression, since nothing is bleeding in from either side. In practical terms the degree matters more for aspects, which depend on precise angles between planets.
Can two people born on 5 January have very different charts?
Yes, easily. They share a Sun to within a degree and can differ in Moon sign, rising sign and every house placement, all of which turn on the hour and the place of birth.