Wǔxíng is usually printed in English as the five elements, which quietly hands the reader the wrong book. The Greek elements are substances: earth, air, fire and water are what the world is made of, and a thing is a mixture of them. 行 is not a substance. It is a going, a course, a phase — the same character as in 行走, to walk. The five are stages a process passes through, each named after the clearest everyday instance of that stage.
Read that way the scheme stops being mystical and starts being ordinary. Wood is the phase in which things push outward and upward: spring, morning, the first surge of an effort. Fire is the top of the arc. Earth is the turn, the settling, the digesting. Metal is contraction and sorting, autumn, the breath. Water is the bottom of the year, storage, the part nobody sees. Anything with a rise and a fall can be described in five stages, and this is a set of names for them.
The list is older than medicine. Its earliest surviving statement is a chapter of the Book of Documents called the Great Plan, in which each of the five gets a one-line description of what it does — water soaks and descends, fire flames upward, wood bends and straightens — and a flavour attached to it. Salt for water, bitter for fire, sour for wood. Those flavour pairings are still in the table lower down this page, unchanged, two and a half thousand years later.