A team has finished a game with 5-12 singles and extra-base hits 6 times since 1897, most recently New York Mets on 6 September 2020. That is about one every 73,834 team-games.
Box score for the most recent one ↗
4-13 5-7 5-8 5-9 5-10 5-11 5-12 5-13 5-14 5-15 5-17 6-6 6-7
The whole distribution — Singles and Extra-Base Hits · All 18 shapes