On the designation of the planets, Quack tells us that:

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“The Egyptians had a strong tendency to differentiate clearly between Sun and Moon, on the one hand (often called “the two luminaries”), and the five planets, on the other. At least for the late (demotic) phase of the Egyptian language, the term the (five) living stars is clearly attested as a specific term for the planets. It is uncertain if living stars also specifically designates the planets in the older periods during which this expression is not yet attested with the specific number five.”

This tells us that Quack expects a planetary designation to be associated with the number five. However, logically, the reverse is not true that any designation associated with the number five is planetary. Per my OP, I am investigating designation related to the House of Thoth which is associated to Hemiunu. According to the Global Egyptian Museum, Hemiunu Khufu’s Vizier held the title:

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"[4] Eldest of the Palace, 'Greatest of the Five' (in [of]) the House of Thoth, who loves his lord, the Sole Friend"

The “House of Thoth” is not just associated with the number five but is also important thread in the Westcar Papyrus, Djedi’s knowledge of the number of chambers of the sanctuary of Thoth is highly valuable to Khufu who wants to use that information for his horizon (Pyramid).

Berrgren argues that the translation of the word “chambers” is insecure and may instead mean something akin to plans, or measurements. Various scholars have reviewed what the sanctuary of Thoth in the Westcar Papyrus may be. Gardiner informs us “I have no light to throw on the whereabouts of the wnt; it may be the name of the sanctuary of Hermopolis Magna, or it may be the name of an earlier sanctuary of Thoth in the Delta; or it may be a purely mythical building”.

Boylan discusses the House of Thoth but doesn’t get any closer to resolving the terms inherent meaning:

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Boylan p148
“The House” (or Temple) “of Thoth” is frequently spoken of in the O.K. (5), and we find in that period the priestly title, or title of dignity, which is later so familiar - “the Great of the five of the temple of Thoth”

Rawash provides an interesting clue to the mystery of the House of Thoth in that we find that it is the place of the sealing of letters:

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Rawash
According to Spell 657 of coffin text52 the house of Thoth is the place where letters was sealed in as follows:
The letter goes out from the house of Re, having been sealed in the house of Thoth, and I have called to mind all the magic which is in this my belly"

The judgement of Horus and Seth sees many letters exchanged as the Ennead in the form of the council of thirty moves between different houses, suggestive of a stellar or solar path.

There is a strong association of Thoth with the planet Mercury which is documented by Quack, providing further evidence that the five House of Thoth may be planetary. One final clue is published by Boylan where he lists on p198 “The Bull of Heaven” as an epithet of Thoth, referencing Brugsch. Quack notes that “The Bull of Heaven” is also a possible attestation of Saturn, also published by Brugsch.

As such, the House of Thoth referenced in the Westcar Papyrus story and in Hemiunus title could well be related to Saturn. What do you think?

Boylan, Patrick “Thoth, the Hermes of Egypt : a study of some aspects of theological thought in ancient Egypt”, p148, p198 accessed from [archive.org]

Gardiner, Alan H. “The Secret Chambers of the Sanctuary of Thoth.” The Journal of Egyptian Archaeology, vol. 11, no. 1/2, 1925, pp. 2–5. JSTOR, JSTOR, www.jstor.org/stars stable/3854265.

Rawash, H. H., The Sacredness of Some Seals and its Relationship to God Thoth, JOURNAL OF The General Union OF Arab Archaeologist, pp76-77

Quack, Joachim, The Planets in Ancient Egypt, accessed from [oxfordre.com]