Charles Ellicott Commentary Daniel 5:7

"The king cried aloud to bring in the enchanters, the Chaldeans, and the soothsayers. The king spake and said to the wise men of Babylon, Whosoever shall read this writing, and show me the interpretation thereof, shall be clothed with purple, and have a chain of gold about his neck, and shall be the third ruler in the kingdom." — Daniel 5:7 (ASV)

The astrologers. It is worthy of notice that on this occasion the magicians (the chartummim) do not appear. We must either suppose that they are included under the general term "Chaldeans," or that the king in his terror forgot to summon them. The "wise men" spoken of (Daniel 5:8) were the body over which Daniel was president—a post which, it appears from Daniel 8:27, he held at this time. It is needless to discuss why Daniel did not come in at first.

The third ruler. See Excursus C. Those who adopt another view of Belshazzar maintain that a triumvirate existed at this time, similar to that in the days of Darius the Mede (Daniel 6:2), and that the king promises to raise to the rank of "triumvir" the person who could interpret the vision successfully. It may be noticed that the form of the ordinal "third," both here and in Daniel 5:16 and Daniel 5:29, is very peculiar, and that in the last two passages it resembles a substantive rather than an adjective.