There is one pre-1805 survivor, but it isn't in Detroit anymore, or even in the U.S.
The Park House in Amherstburg was built in what's now Detroit around 1794 [[probably around Delray). However, the owners were British loyalists and when Detroit and surrounding territory were ceded by the British to the U.S. in 1796 [[under the Jay Treaty that settled unresolved issues from the American Revolution) they found themselves living in a country they wanted no part of. So, around 1798, the house was disassembled and moved by canoe across the river to Amherstburg, to a site on Dalhousie St in the middle of town. There it had several owners over the years, including, for a little over 100 years, the Park family for whom the house in now named.
In 1972 the house was moved again, a few blocks north on Dalhousie to the King's Navy Yard Park, where it stands today as the oldest structure in the greater Detroit-Windsor area and is open to the public as a museum.
https://en.wikipedia.org/wiki/Park_House_Museum
http://www.puredetroit.com/index.php/history/detroits-oldest-house-is-in-canada-321.html
http://www.parkhousemuseum.com/
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