Safety play. You want to nudge their 5 to where it's about on the right 1 on the 11 and leave the CB so they can kick off the end rail. Let them break up your problem. If they are good at safety play and just barely hit the 11 for rail contact, you have the 7 as an insurance ball. Now if this happens, don't make the 7, but push it close to the side pocket for a duck and leave them on the opposite end rail behind your 5. Make them kick it again with more distance and with the CB frozen on the end rail if possible. In this situation you should be a favorite to win, but make sure it's a sure thing before attempting. Don't leave them any banks on the 11 because they just might get out out of desperation. This includes a cross bank down table from where the 7 is.
EDIT: If they give you BIH by missing their hit on the 11, simply float the 7 to block their pocket and leave them no bank. The 7 is now a duck. The game is won, give them the opportunity to make it easier for you and more frustrating for themselves. Repeat until 3 foul rule or let them sell the farm with a hero attempt.