How much does should it cost to demo a large shed?

I am buying a home that has a large shed in the back. The loan is FHA and the appraiser requires it be torn down or repaired. This is an old shed close to 100 years old and was built with all 2x4s with many rotting pieces so fixing it would cost the same as rebuilding a new one. The shed is approx 15x24 in an L shape. I'm working with a contractor for the other repairs and he quoted me at $7,500 for a full demo, I said leave the floors and he brought it down to $5,500. This seems like a rather large amount especially looking around online I was expecting 2-3k at most. Is his quote realistic? Im under a deadline so I had him write it up but I most likely will do it myself or find someone with a excavator to come in and just crush it.

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