Does anyone have experience selling a domain name worth more than $5,000? How should I sell a valuable domain I own?

I don't have experience selling a domain at that range, but I've come close.

Are you asking how to find sellers, or more like how to take care of the payment, contracts, etc?

I've used to both sell and buy domains. It's a safe to transact if you don't know the buyer.

To find a buyer I'd make sure that you're easily reachable by anyone checking out the domain. So make sure your email address listed in the whois data is working, and optionally put a page up stating the domain is for sale with a way to reach you. This way it's more likely you'll end up selling to and end-user versus a domain trader. End-users tend to have higher budgets because they are specifically looking for that domain.

That said, it's worth also listing your domain on sites like Sedo and NamePros. I think Sedo has some partnership where your domain will be listed as "For Sale" with certain domain registrars when people search for your keyword. So that's another nice way to find end-users to sell to.

I don't have experience proactively reaching out to potential buyers. I imagine anything that communicates you're looking to sell will disadvantage you during negotiation, but then again the negotiation might never ever happen if you don't reach out.