A team has finished a game with 6-5-3 runs-hits-errors line 21 times since 1897, most recently Colorado Rockies on 25 June 2003. That is about one every 21,095 team-games.
Box score for the most recent one ↗
6-4-4 6-4-3 6-4-0 6-4-5 6-5-2 6-5-1 6-5-3 6-5-5 6-5-0 6-5-6 6-5-4 6-5-8 6-6-1
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes