A team has finished a game with 0-3-5 runs-hits-errors line 34 times since 1897, most recently Detroit Tigers on 6 September 1980. That is about one every 13,029 team-games.
Box score for the most recent one ↗
0-3-1 0-3-0 0-3-4 0-3-3 0-3-2 0-3-6 0-3-5 0-3-7 0-3-8 0-4-1 0-4-3 0-4-2 0-4-0
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes