A team has finished a game with 0-1-5 runs-hits-errors line 10 times since 1897, most recently Chicago White Sox on 26 August 1992. That is about one every 44,300 team-games.
Box score for the most recent one ↗
0-1-2 0-1-0 0-1-3 0-1-1 0-1-6 0-1-7 0-1-5 0-2-1 0-2-3 0-2-2 0-2-0 0-2-5 0-2-6
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes