Five is where the notation changes. One to four are written as dots; five is written as a single bar, and every coefficient above it is built from bars and dots together. The bar-and-dot system is shared across Mesoamerica and appears on monuments from well before the Classic Maya period.
Five also governs the relation between the two calendars. A 365-day Haab year advances the Tzolk'in day sign by five places, because 365 leaves a remainder of five on division by twenty, and that single fact produces the four Year Bearers, the fifty-two-year Calendar Round and the restriction of any given Haab position to four of the twenty signs. Five is doing more work in the Maya calendar than any other small number.
Maya numerals are written with a dot for one and a bar for five, and the coefficient of a day is written in exactly that way in the inscriptions, set beside the day sign in its cartouche. The system is positional and includes a sign for zero, which is why the Long Count can be written as a string of places, but within the 260-day count no number above thirteen ever occurs and the notation stays simple.
Overtone, the name given to this coefficient in modern popular writing, comes from the Dreamspell devised by Jose Arguelles and published in 1987. It has no counterpart in Maya sources, where the coefficient is the number five and is written with one bar.
Sources Maya Hieroglyphic Writing: An IntroductionJ. Eric S. Thompson with Dreamspell: The Journey of Timeship Earth 2013Jose Arguelles