Leaving PhD in the 6th year and apply for a new PhD program
You don't give us much to go with. What you are proposing sounds pretty dramatic, and it potentially has a lot of factors going against you: Based on your description, it seems that 1) you are abandoning a Ph.D. very deeply into it; 2) you are parting ways with your adviser unamicably; 3) you are applying to a highly competitive program in the United States; 4) you may not have publications. The one thing potentially weighing in your favor is the fact that you've interned at that university: If your adviser-to-be is willing to commit to advising you and supporting you financially, it may override the other concerns in the eyes of the department.

Someone above suggests applying yourself to completing your Ph.D. and then seeking a postdoc in your dream area; that could well have better odds of success in the long term. Ultimately, of course, there's no way we can predict what the outcome will be. I'd suggest that you be sure you are being completely honest with yourself about the reasons for the situation you find yourself in, and what it is you are trying to accomplish by starting anew.