In the third of a series, the author describes how symmetrical quintic functions can be expressed in three equivalent formats--like other symmetrical functions. Quadratic functions have a line of symmetry through their vertex and cubic functions have 1800 rotational symmetry around their point of inflection. However, polynomial functions of degree greater than three can be both symmetrical and asymmetrical (Goehle & Kobayashi, 2013). This work considers algebraic conversions of symmetrical quintic functions and shows the ways to express them in three equivalent formats (as is the case with quadratic and cubic functions and shown for symmetric quartic functions in Miškovic (2021)).