A team has finished a game with 23-5 singles and extra-base hits 1 time since 1897, most recently New York Mets on 4 July 1985. That is about one every 443,004 team-games.
Box score for the most recent one ↗
22-3 22-4 22-6 23-0 23-2 23-4 23-5 23-6 23-10 24-0 24-3 25-2 25-3
The whole distribution — Singles and Extra-Base Hits · All 18 shapes