I would say go where you really want to go. 5k is not a loan that you will drag all your life. Plus you can probably find loans that you can apply along the way to cover the rest of your expenses, or even ask the school for some more funding right now.
Or looking at it from another angle, what would you regret the most? Not going to Berkeley because you had a little bit more money elsewhere, or will you regret having more debts after your studies? If you were looking at 30 or 60k debts versus a full ride elsewhere, it would be a different story.