A team has finished a game with 5-15 singles and extra-base hits 2 times since 1897, most recently New York Mets on 24 August 2015. That is about one every 221,502 team-games.
Box score for the most recent one ↗
5-9 5-10 5-11 5-12 5-13 5-14 5-15 5-17 6-6 6-7 6-8 6-9 6-10
The whole distribution — Singles and Extra-Base Hits · All 18 shapes