  We present an alternative relatively easy way to understand and determine the
zeros of a quintic whose Galois group is isomorphic to the group of rotational
symmetries of a regular icosahedron. The extensive algebraic procedures of
Klein in his famous \textit{Vorlesungen \"uber das Ikosaeder und die
Aufl\"osung der Gleichungen vom f\"unften Grade} are here shortened via
Heymann's theory of transformations. Also, we give a complete explanation of
the so-called icosahedral equation and its solution in terms of Gaussian
hypergeometric functions. As an innovative element, we construct this solution
by using algebraic transformations of hypergeometric series. Within this
framework, we develop a practical algorithm to compute the zeros of the
quintic.
