For the most part, if you have already invested 5 years in your current university and have an advisor, then it is not worth relocating. In general, the following hold true at that point in your career, although if not for you the answer may be different.
- You already have an advisor, so any additional classes are not really going to help you that much. Faculty will not treat you the same as if you were eventually a potential student, which is not to say the treatment will be bad, but they won't put to much time into you.
- You are coming "pre-programmed" with your older schools viewpoint, mannerisms and ideology, and you're not likely to shake that. At this point in your career, you are half-baked as a grad student, meaning that you are already representing the school you are at. You might be able to fit in at the new program, but if it isn't that different then all the new work isn't worth it, and if it is that different, then you are not likely to succeed.
- You most likely will be thought of as being from your original school anyway. The relationships that you build in grad school are part of your success later on, and you already missed the boat with the cohort you would hope to graduate with. Things like ongoing projects can help that, but in the end, when you are on the market and in the field, you will be a student of your first program.
- There are a lot of costs associated with moving that can really set your timeline back outside the costs of changing a program. Now you know the library. You know the labs. You know the people in the department. Once you move that will no longer be true, and that is a cost. Add into all of that the actual time and monetary costs of a move, which will kill at least several thousand dollars and a month of your time. A month over a summer can mean the difference between being ready to go on the job market in the fall, and having to wait another year, which can be fatal on the job market, depending on your specialization.
- There is a lot of attraction to trying new things, but in the end grad school is a means to an end, not the end itself. Get a job/post-doc and go through that there, not as a grad student. In fact, there is no reason you cannot graduate from your current school, and then go work with your advisor at his new program as a post-doc, or better yet Asst. Prof! Get the degree done.
There is one thing that could veto all that however: sometimes when your faculty advisor leaves, it is like they were kidnapped by aliens, and you never hear from them again. That can really put a kink in completing the program at all, and has ended many promising careers. Ensure before you faculty departs that you have a plan to graduate.
Ideally, in my field, I would say that you have a proposal complete with a couple of chapters of your dissertation written. If you are in the natural sciences, you should already be running your experiments and collecting your field data. If you are still developing your project, you may not be able to complete that work if your advisor is too far, or difficult to get ahold of. Make sure you have a long conversation with your advisor about this before you make any decisions.