The Milwaukee Brewers are the only undefeated F5 (1st 5 Innings) MLB team with a perfect 5-0 record. Their overall full game record is 4-1.
Interestingly, the Houston Astros are the 2nd best F5 team at 6-1, but their full game record is 2-5. You need great starting pitchers and an iffy bullpen to accomplish that.