Five village leaders, one per great nation — a numbered set that exists to make a map legible rather than to rank a fight.
Filed by its count, not its title
Reduced as a phrase, “The Five Kage” would sit on The Closing — but that would be reducing wording this reference chose. The set is filed under 5 · The Turn instead, because 5 is what its author chose, and a chosen number outranks an imposed one.
The heads of the five great hidden villages, one each for the nations of Fire, Wind, Water, Lightning and Earth. Each title is an office, held in succession, rather than a personal rank.
Five here is doing geography, not power scaling. The set exists so a reader can hold an entire world's politics in mind at once: five nations, five leaders, five sets of interests. Any smaller and the world feels provincial; any larger and a reader stops tracking who is aligned with whom.
Because the seats are offices, the number survives its holders. That is unusual in shōnen numbered sets and it is what lets the series run a summit meeting — a scene type that requires the participants to be equals with incompatible interests, which a ranked set could never supply.
The elemental assignment follows the Chinese five-phase system (wood, fire, earth, metal, water) as it was absorbed into Japanese thought, adapted here to the five chakra natures. It is the most common organising five in the medium, and it is why so many manga worlds have exactly five of anything.