This does not sound right as the compressor is about $350 to replace so I am not sure what would be more then $5,000.00. Unless they are replacing the entire system including the lines, I don't think that is something I would pay for.
The expansion valve does not change the repair if the compressor needs to be replaced so I would seek a second opinion based on this info.
Here are some guides that will help with this replacement:
https://www.2carpros.com/articles/replace-air-conditioner-compressor
https://www.2carpros.com/articles/re-charge-an-air-conditioner-system
Let's run through the attached info below and let us know if you have questions. Thanks
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Sunday, January 31st, 2021 AT 2:10 PM