How much is enough for a down payment to shave a few thousand off a car?

I'm planning to buy a used vehicle. I'm currently looking at one costing $22,900. I would ideally like pay $19,000 after tax included (so I would have to get it down to 17ish before tax.) I've never bought a vehicle from a dealership so I have no idea how much dealers can cut off the lot price on a used vehicle. I know trying shave off 5 grand is a long shot but I'm willing to pay around $20,500 after tax for the car. I planned to finance for 48 months on the vehicle for the rest of the amount so they'll make some money off me from that. I've currently got 5 grand for a down payment but am I gonna need a few more thousand to be looked at seriously?