A team has finished a game with 0-2-5 runs-hits-errors line 20 times since 1897, most recently Chicago White Sox on 21 August 1988. That is about one every 22,150 team-games.
Box score for the most recent one ↗
0-1-7 0-1-5 0-2-1 0-2-3 0-2-2 0-2-0 0-2-5 0-2-6 0-2-4 0-2-7 0-3-1 0-3-0 0-3-4
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes