A team has finished a game with 3-5-7 runs-hits-errors line 6 times since 1897, most recently Chicago Cubs on 12 May 1932. That is about one every 73,834 team-games.
Box score for the most recent one ↗
3-4-8 3-4-6 3-4-4 3-5-1 3-5-2 3-5-4 3-5-7 3-5-0 3-5-3 3-5-9 3-5-5 3-5-6 3-6-1
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes