My longest winning streak was 18 games in OOTP4, but haven't approached that in 5. I'm not sure I will with the financials being tougher in manager mode now. As much as I wanted to "stay honest," it was too easy after blowing a negotiation with my stud pitcher to "extend" his existing contract one more year to give me another crack at it the next season...
I think the longest streak I've had in OOTP5 is 9 games.