A team has finished a game with 0-5-6 runs-hits-errors line 17 times since 1897, most recently Houston Astros on 30 July 1979. That is about one every 26,059 team-games.
Box score for the most recent one ↗
0-5-4 0-5-1 0-5-7 0-5-9 0-5-5 0-5-12 0-5-6 0-5-10 0-6-1 0-6-0 0-6-4 0-6-3 0-6-6
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes