Picture is courtesy of Dr. Asher Eder who shot it about 40 years ago in Capernaum, where he used to guide tourists.

The following paragraph is from Dr. Asher Eder’s book The Star of David, which was published in 1987 in English in Jerusalem by Rubin Mass Ltd. The publication here is courtesy of Oren Mass
This version includes corrections and new materials that do not appear on the printed version

In ancient times and in the Middle Ages, the five-pointed star, or pentagram, was also called the Shield of David, or Star of David, while the hexagram was sometimes called "Solomon's Seal".We shall deal briefly with the pentagram symbol.
As far as we know, 6th-Century Byzantine scholars were the first to speak of the pentagram as the Shield of David, while in the Middle Ages this idea was occasionally taken up by Jews and Muslims as well.
Judging from archaeological evidence, artists were drawing pentagrams long before they started drawing hexagrams. One of the oldest known artifacts is a clay jug with a pentagram painted on it, found in Jamdad Nasr (modern-day Iraq) and dated to the 4th millenium B.C.E.
Similar designs were found in Megido, one on a seal dating from the 19th Century B.C.E., the other on a clay jug, dated 17th Century B.C.E.
One of the many other findings worth mentioning is the impression of a pentagram on a jar handle - probably an official seal (possibly royal) in the Kingdom of Judah. In its angles appear the word "Jerusalem", written in ancient Hebrew characters. Fine examples can also be found on Celtic brooches:
Another outstanding example is a pentagram carved in stone, with disks in its five angles. It can be seen in the ruins of Kfar Nahum, in the following design
Although no other known design of this type exists, the five disks in the angles of the star may well symbolize the five planets known in ancient times, pointing to the astronomical connotations of the design.
In ancient times, the pentagram was indeed the sign of those initiated into the wisdom of astronomy and astrology. Priests imbued with this knowledge calculated the calendar with its agricultural and religious seasons. It is for this reason that the ancient Babylonians were known as Chaldeans - still a byword for astrologers, for their religion was based upon such calculations.
All in all, the pentagram can be seen as a symbol for nature, i.e. the material aspect of Creation. This would be supported by the fact that the entire pentagram can be drawn without lifting pen off paper, while the interwoven hexagram depicts polarities in their balance requires that its two triangles be drawn separately. (To be sure, one could draw the hexagon first and then add the six outer triangles without lifting the pen, but that would not do justice to the meaning of the symbol). – Interestingly enough, the ancient Pythagoreans gave the name “health” to the pentagram. It was probably before this background that later on it went into magic.
True, the Jewish people in their worship of the Creator of Heaven and Earth also had to develop a calendar based on the "lights in the firmament of the heavens to separate the day from the night, and to be for signs and for seasons and for days and for years..."(Gen.1:14), so it should not be surprising to find the figure of the pentagram with the five disks in a synagogue next to the six-pointed star (see fig.6-8); nor should it be surprising that the five-pointed star is often called Solomon's Seal4. The Tanakh says Solomon was renowned for his wisdom5 in both heavenly and earthly matters, and this could explain why the five-pointed star as a symbol of wisdom was attributed to him, and named after him. However, we should keep in mind that the termמגן , magen, shield, is used in connection with Abraham and with David, while the term חותם , hotam, seal, is used in connection with Solomon irrespective whether the pentagram or the hexagram is related to him.

Solomon, Seal of
Joseph Jacobs and M. Seligsohn wrote in the Jewish Encyclopedia the entry Solomon, Seal of.
I bring it here - I only added the headings…

A. Source: The Jewish legend
The legend that Solomon possessed a seal ring on which the name of God was engraved and by means of which he controlled the demons is related at length in Gittin 68a, b.

B. Arabic development of the Jewish legend
This legend is especially developed by Arabic writers, who dec1are that the ring, on which was engraved "the Most Great Name of God," and which was given to Solomon from heaven, was partly brass and partly iron. With the brass part of the ring Solomon signed his written commands to the good genii, and with the iron part he signed his commands to the evil genii, or devils. The Arabic writers dec1are also that Solomon received four jewels from four different angels, and that he set them in one ring, so that he could control the four elements.

C. Another legend
The legend that Asmodeus once obtained possession of the ring and threw it into the sea, and that Solomon was thus deprived of his power until he discovered the ring inside a fish (Jellinek, "B. H." ii. 86-87), also has an Arabic source (comp. D'Herbelot, "Bibliothèque Orientale," s.v. "Soliman ben Daoud"; Fabricius, "Codex Pseudepigraphicus," i. 1054; and see Solomon in Arabic Literature).

D. Josephus
The legend of a magic ring by means of which the possessor could exorcise demons was current in the first century, as is shown by Josephus' statement ("Ant." viii. 2, § 5) that one Eleazar exorcised demons in the presence of Vespasian by means of a ring, using incantations composed by Solomon Fabricius (l.c.) thinks that the legend of the ring of Solomon thrown into the sea and found afterward inside a fish is derived from the story of the ring of Polycrates, a story which is related by Herodotus (iii. 41 et seq.), Strabo (xiv. 638), and others, and which was the basis of Schiller's poem "Der Ring des Polykrates."

E. Six-pointed star
The Arabs afterward gave the name of "Solomon's seal" to the six-pointed star-like figure (see Magen, Dawid) engraved on the bottom of their drinking-cups.

F. Table of Solomon
It is related in the "Arabian Nights" (ch. xx.) that Sindbad, in his seventh voyage, presented Harun al-Rashid cup on which the "table of Solomon" was represented; and Lane thinks that this was the figure of "Solomon's seal" (note 93 to ch. xx. of his translation of the "Arabian Nights").

G. Pentacle
In Western legends, however, it is the pentacle, or "druid's foot," that represents the seal. This figure, called by Bishop Kennet the "pentangle" of Solomon, was supposed to have the power of driving away demons. Mephistopheles says to Faust that he is prevented from entering the house by the druid's foot ("Drudenfuss"), or pentagram, which guards the threshold ("Faust," in Otto Devrient's edition, part i., scene 6). The work entitled "Claviculæ Salomonis" contains treatises on all kinds of pentacles. The tradition of Solomon's seal was the basis of Büschenthal's tragedy "Der Siegelring Salomonis," specimens of which are given in "Bikkure ha-'Ittim," v. 3 et seq. (German part). A work regarding a magic signet-ring is ascribed to Solomon (see Solomon, Apocryphal Works of). See also Asmodeus; Solomon in Rabbinical Literature.