I switched advisors during my PhD. However, I had chosen my university specifically because there were several profs doing work in my tiny niche field of interest, knowing that an advisor switch is sometimes unavoidable.
Funny enough, I don’t even work in that chosen niche anymore because my eventual PhD project was in a better-funded, larger field.
Here are a few questions it would be helpful for you to answer:
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What is your general field of study (you don’t need to get too specific).
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How much data have you collected and analyzed? Are these collected data for the ill-fated PhD project or for something else?
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What did your committee say about your progress at your most recent meeting?
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Do you already have a specific advisor in mind at another university? Is that person committed to taking you on and providing funding for you? Would you bring your project with you somehow, or would you be starting fresh?
In my opinion, 5 years is too far along to make such a drastic switch unless you truly have no other option. I fear it may not yield the results that you are hoping for. You should be finishing up right now (not to put more stress on you). Here are things I’d explore before committing to switching institutions:
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Talk with your committee about your conundrum. They are there to help you. If they are not helpful, consider adding a committee member who would be helpful.
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If you’ve already collected a lot of data, try to use as much of that as you can for a dissertation project.
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Can you switch projects but keep the advisor?
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Can you keep the project or something close to it but switch committee chair and keep your current one on the project as a collaborator or co-chair?
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Can you start a new project with a new advisor at your current institution?
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Do you have enough data collected/analyzed to “master-out”?
I will say this: at least in my field (bio/medical), I struggle to think of a scenario where I or anyone I know would take on a 5th year PhD student from another university. There would have to be some major extenuating circumstances for me to even entertain the idea. Like maybe I collaborate with their lab and they’ve already collected a bunch of data and they just need a different advisor to shepherd them across the finish line, but their existing advisor remains part of the collaborative project.
I’ve learned that the exact subject that I’m studying is less important than I once thought it was. I can be happy studying a wide variety of things. Far more important is that I am working with people that are a good fit for me, and there is sufficient funding to do the work. It sounds like your advisor might not be a good fit for you, but switching universities entirely is a drastic step at 5 years and you should definitely seek advice from several professors you trust and consider all the alternatives before trying to move in that direction.