Where the published numbers come from
A stated solar degree is always a measurement of a specific instant. Most published figures use noon, and many use noon in universal time without saying so, which is already an hour or two away from noon where the reader was born.
On 5 December the noon Sun has occupied roughly twelve and two fifths to thirteen and four fifths degrees of Sagittarius across the years from 1930 to 2035. Any single number quoted for the date is a point inside that band, and which point depends entirely on the year chosen.
So two sources differing by a degree have almost certainly picked different years. The disagreement is real and it is uninteresting, and it disappears the moment a calculation is run for an actual birth rather than for a generic date.
The mechanism behind the spread
A tropical year runs about a quarter of a day longer than a common calendar year. Each ordinary year the Sun therefore reaches a given longitude roughly six hours later against the calendar, which shows up as a slightly smaller degree on a fixed date. Every fourth year the leap day pulls it back by close to a full day.
Repeated, that produces a sawtooth about a day wide, which is where the band comes from. The calendar and the orbit stay in step because the drift and the correction are designed to cancel, and the small residue left over is handled by the Gregorian rule that skips leap days in most century years.
A birth time adds its own spread on top. The Sun moves a little under a degree a day, so a birth at midnight sits about half a degree from the noon figure, and a birthplace on the far side of the world shifts the universal time by hours.
What thirteen degrees fixes
The sign is settled and was never otherwise, since thirteen degrees is well inside Sagittarius with a fortnight of margin in both directions. What the degree does settle is the face: this is the second decan of the sign, running from ten to twenty degrees.
The Chaldean order gives that face to the Moon, the triplicity scheme gives it to Aries and therefore to Mars. Tradition reads the Mars version as the sign's opinions turned into positions and acted on quickly, and the Moon version as the same restlessness anchored to people and to familiar ground.
Both are interpretations rather than measurements. The reason to have the degree is that the face follows from it arithmetically, and so do the aspects the Sun makes to everything else in a chart.
The limits of any birthday page
Even a precise solar degree leaves most of a chart untouched. The Moon can be in either of two signs on this date depending on the hour, because it covers around thirteen degrees a day. The Ascendant cannot be estimated from a date at all, since the whole zodiac passes the horizon every twenty four hours.
That is worth stating plainly rather than hiding. Everyone born within roughly a month shares the sun sign, so it is the layer of a chart with the least to say about an individual, however exactly it is stated.
The widget above calculates the position for your own year, hour and birthplace, and reports how far the result sits from the nearest sign boundary. It will not match a table exactly, and that is the point: a table is a summary and a calculation is not.
Questions people ask about this
What is the solar degree for 5 December?
Around thirteen degrees of Sagittarius, with the noon figure ranging from roughly twelve and a half to nearly fourteen across the years on record. Your own value depends on year, hour and birthplace.
Why does another site give a different degree?
Almost always because it quotes a single year, or noon in a time zone it does not name. Both figures can be correct for the instant each describes.
Is the sign ever in doubt?
No. Thirteen degrees is comfortably inside Sagittarius, with about a fortnight to the boundary in either direction.
Which decan does 5 December fall in?
The second decan of Sagittarius, from ten to twenty degrees, with several degrees of margin at both ends.
Does the noon convention matter?
It matters at the level of half a degree, which is enough to change a close aspect and not enough to change a sign or a face on this date.
What would make the answer more accurate?
A recorded birth time and the town of birth. Together those remove both the year assumption and the noon assumption from the calculation.