Unfortunately there is never a short answer(or I can't find it)..so bear with the rambling on.
Selling to dealership's is convenience(that is what you are paying for) and they take the car off your hand right away and you drive away with the new car. If your driveway can only really store one car conveniently(many apartment dwellers only have 1 parking space so they have no place to store the old car while they try to sell it. If you OWN(NOT RENT) a house, or you have an understanding lenient LL(some of those type of people exist) who has say not super neat, super tight apartment grounds(meaning he has extra parking spaces) you can work out an arrangement to let your old car stand there for a week or 2 while you clean it up and actively try to sell it...which is easier if it is a very busy area with a lot of traffic flow. They see the sign in the window and the price and your phone number and they give you a call. Not all people are great salespeople so do not want to do that kind of work. but if you have the "gift" of gab and you can make people comfortable talking to you, and they will be talking about the car...so you need some knowledge...which you do have through experience..."It gave me no troubles, ever; or what I did have I also had it fixed...so no problems.
..I did not build the car so I personally do not have a warranty on it; I look to the manufacturer if an issue shows up...as they do what they can do.
..It runs good, I just need a different STYLE of car because I got a larger family or work situation has changed or I wanted 4 door instead of 2 for convenience, or I need different because my job is different so I need to carry tools and stuff and this CAR won't serve that purpose for me. I am forced to look at a truck or van or SUV or crossover. If I could have 2 cars I would still keep "Betsy".
. The reasons for selling can be many. Me, I did it because I wanted to drive a different type or make of car and I wanted a change in color.
(but that is my personal reasons which is only my business)
So even selling your car privately, you are going to take a hit "a loss" as cars do not go up in value.(it has to be a collectible vintage that is desired) & not all cars fit that description.
$2500 more is really OPTIMISTIC on your end. Not really reality.
Some dealerships are like that relying on the brand name to allow them to ask more. Say for example VW, their prices are quite high for their new cars and when you compare car to car with its features, I can get just as much if not more from a HONDA vehicle than(for less money) than I could from a VW. I chose to buy a HONDA instead. I knew the repair record on the VW was quite good(as many of my previous cars were VW so I was tooled and knew how to fix most minor problems. But for less money the HONDA proves to be just as good.
While you can price your car at $2500.00 more, there is no guarantee you will have any takers. You may have to wait until school starts or some other event or just be lucky because somebody WANTED THAT EXACT CAR OF THAT YEAR. So you got a bite. They must pay for it in cash to you, the full amount because you are not a Loan Company so you are not taking payments. (something the car dealers are willing to do to make a sale) They can't offer any warranty either but they make it sound like they are and "had the car checked over by their mechanic" never saying that their mechanic is the clown that fills the balloons with hot air.
. You are competing with the lot. The one advantage you may have is that you are not paying for the lot the car sits on. Car lots pay rent so every car sale, some of that money goes to rent and advertising and paying salesman's wages and the "clown" & lighting and insurance for the Lot to insure themselves in case someone hurts themselves on the lot property and sues the car lot...etc[they got a lot of expenses] which is why they got to move cars so they do not sell them at sticker price for those hard to sell customers...but getting SOME money is better than NO money.
. You do not have those expenses so you are not in a rush to sell so fast.
You can wait for the right fish to bite at your hook.
It is like fishing or hunting....nope don't want that deer as the rack is not big enough, we will wait until a big one shows up. It will happen if you wait long enough for they say "A sucker is born every minute"
Are you willing to wait for something that may or may not happen.?