Felix Klein, <A HREF="https://link.springer.com/content/pdf/10.1007/BF02297507.pdf">Über die Transformation der elliptischen Funktionen und die Auflösung der Gleichungen fünften Grades</A>, Math. Ann., vol. 14,‎ 1878-1879, p. 111-172.

There is also a slightly earlier publication in Italian, *Sull' equazioni dell' Icosaedro nella risoluzione delle equazioni del quinto grado*, Reale Istituto Lombardo, Rendiconto, Ser, vol. 10, no 2,‎ 1877.

<IMG SRC="https://ilorentz.org/beenakker/MO/Klein.png" WIDTH="400"/>

Dedekind may have gotten there first, see <A HREF="http://www.neverendingbooks.org/dedekind-or-klein">Dedekind or Klein</A>