My first penta-kill was in a normal game. About 400th normal game, playing as Jinx. Worst part was it was a 4v5 where I got a penta, and we still lost.
Second was in roughly my 300th ARAM, playing as Ahri.
Third was shortly thereafter in an ARAM on shyvana when I had never played the champion before (still no idea how that happened).
Fourth was again on Jinx in a normal game.
Fifth was on Hecarim in a normal game, finally after I had what would have been my second penta-kill brutally stolen from my by a teammate (solo the triple kill, secure the 4th kill with a teammate, force the last enemy to Zhonya's at under 10% hp and my mid laner arrives and times his spell for right as they exit stasis...)
Sixth was on Jinx in a ranked game (around 50th ranked game).