Firstly thanks to ANONYMOUS1999 for some a heartfelt warm welcoming contribution, it holds all the promise of a world-about-us positive road ahead.
And so to another.....
Fives in music as an extension of the jaunty little image in the original post presents an interesting spread of numeric ideas, of course music is distinctly intertwined with Cosmology and the mathematical/numerical elements within that area of study, but that perhaps is a tangential story for another day.
Two powerful examples, although there are significantly more, that emerge from musicality are:
Ninth Chords in Harmony and
the Circle of Fifths.
In music, harmony considers the process by which the composition of individual sounds, or superpositions of sounds, is analysed by hearing. Usually, in musical composition terms this means detecting or devising simultaneously occurring frequencies, pitches (tones and notes), or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. However in it is the size and magnitude of note tonalities in use in the stack that govern final chord numeric assignments, not for the number of chord member notes: thus a ninth chord has five members [tonic, 3rd, 5th, 7th, 9th], not nine.
Rameau's 'Traité de l'harmonie' (Treatise on Harmony) from 1722
In music theory, the circle of fifths (there is also a circle of fourths which is equally important) defines the relationship between the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys. Examining this more specifically, the circle is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale residing in pitch class space. The term 'fifth' defines an interval or mathematical ratio which is the closest and most consonant non-octave interval. The circle of fifths is a sequence of pitches or key tonalities, represented as a circle, in which the next pitch is found seven semitones higher than the last.
Nikolay Diletsky's circle of fifths in Idea grammatiki musikiyskoy (Moscow, 1679)
