I wouldn't back down. It'* too early in the game.
But, at the same time, holding out may cost you more in the end because you might sell it less than $5,500 or even $5,000...plus you have the carrying costs.
This is the WORST time of year to sell a car. I had our Grand Marquis for sale for 2 months and had several offers for $5,400. I stood firm with $5,600 and nobody would offer that much. Standing firm cost me in the end. A lot. The next best offer I got (and the fact I wanted it out of my hair) was for $4,400. I bit the bullet and let it go. Learned a lesson, and don't have the insurance costs...not to mention was able to pay off the loan on the GS.
Be practical. But, remember, everyone and I mean EVERYONE comes with a story.