Why not three or five?
stability plus it carries over from horse drawn wagons
Some do have 3 wheels. But four is much more stable.
Five doesn’t buy you anything.
There are many vehicles with six or more wheels.
There have been plenty of three wheeled cars. This is why most people don’t want one. 
There have been some three wheel configurations with the single wheel in the back instead of the front, which is a bit more stable. If you single wheel steers, then stability is an issue. If the single wheel drives, poor traction becomes an issue.
A four wheel configuration is much more stable.
A fifth wheel doesn’t really add anything useful, and makes steering a bit more difficult.
There are plenty of 6 wheel vehicles.
EDIT: Nevermind, that was a bit more off topic than I meant it to be.
I think we can assume that the OP realises that four-wheel configurations are more stable. The question is, why? It’s a matter of geometry. With three points of contact, any horizontal force perpendicular to a line formed by two of the points can make the structure tip over, and will only be resisted by the remaining point if it is on the far side of the line, which half of the time it won’t be. With rectangular four-wheeled structures, however, there will always be a wheel on the other side of the line. It needs four wheels for this to be true.
Most cars have 5 wheels.
British rednecks. now I’ve seen everything.
Most have 6 or 7. Spare. Flywheel. Probably more.
Not anymore…
Don’t forget the steering wheel.
This is also why a motorcycle with a sidecar is less stable than one on two wheels.
Also all the round gears which will roll like wheels just as well as a steering wheel, if not better.
Hows this for a 5th wheel
The Aptera has three wheels.
If you think it looks like a airplane without the wings, that isn’t an accident. It has a very low drag coefficient. It make the Prius look like a brick.
A 3-wheel vehicle can be very stable if the vehicle itself is tapered towards the 1-wheel side - i.e. no weight hanging off on either side of that single wheel. Like the Morgan trikes, or my velomobile for that matter. But that means making the vehicle narrow on one end, which is good for aerodynamics but an inefficient use of space. A rectangular shape is much more efficient use of space, (maximizes passenger and cargo space).
Additionally, a 3-wheel configuration means one of the wheel wells is right in the middle of the engine compartment or the trunk, which makes for an awkward layout.
Also, on a 3-wheel vehicle, the center wheel is at the center of the road. This can be an issue on unpaved or snowy roads, where there are two smooth ruts, and the middle is rough or snow-covered.
Yet another possible issue is the difficulty of replacing the center wheel in case of a flat tire.
I responded to a poster who said cars have five wheels (wherein one assumes they were already adding the steering wheel in as the fifth wheel).
But thanks for playing.
I have a lot of miles on a sidecar rig.
No, gravity will resist the force even if the added wheel is on the same side that the force is coming from. It takes a bit to lift a sidecar on a motorcyle, or the outrigger on a canoe.
Well not quite. It is actually more stable when the side car lifts…it becomes a two wheeled vehicle. Just a motorcycle with a really fat date hanging off the side. The other way, they tend to “high side” or “turn turtle”. Once the rear wheel of the motorcycle lifts, it ground loops like a taildragger airplane. If you survive the first time that happens, you make damn sure it never happens again.
Any number of wheels is going to tip on a line between two of those wheels.
If you draw a polygon between all the wheels of vehicle, the stability can be well estimated by the area of the polygon, how well centered the weight is, and how high it is.
Here are the issues with three wheeled vehicles:
Three wheeled vehicles feel tippy. How can that be. Since a milk stool is so stable? you ask:
If you slide that milk stool down a road, the seat is going to tip every time any of the three legs drops in a pot hole, and there is nothing to keep the leg from dropping into a pot hole, because each leg has to support it’s share of the weight, or the stool falls over. (OK there is some weight shift due to tipping, but it is minimal for small tip angles) You can try to mitigate this dynamically with soft, long travel suspension, but that makes the rig feel even more tippy.
With a four wheeled vehicle, one wheel can mostly un-weight as it passes over a pot hole. This means that corner of the vehicle will drop much less than the depth of the pothole.
Tricycle or tadpole three wheelers suffer because most of the other vehicles make two tire tracks. This leaves one wheel of the three wheeler running on a high ridge between the ruts in the road, which is also greasy and littered with FOD. This is bad if it is your steering wheel like on a trike, and also bad if it is your power wheel like on most tadpoles. I have seen one tadpole built from the front end of a Subaru FWD car that avoided this…the rear wheel neither steered nor drove.
Sidecars avoid this at the expense of wicked asymmetrical handling. (totally different technique and limitations between left and right turns, pulling one direction on acceleration, pulling to the other when braking.)
More than 4 wheels:
The issue with more than 4 wheels, or not putting the wheels in a rectangle, is that fancy steering geometry is required to prevent some of the wheels from skidding when cornering. The old ELF formula one car had such fancy steering, but many 6 wheelers just skid steer like a tracked vehicle. Speaking of which, tracked vehicles are N wheeled vehicles…they just have a track between the ground and the wheels.
You can have skidding issues with any number of wheels >2:
For stability a sidecar wheel is normally ahead of the rear wheel of the bike by a fair amount. This forces some skidding in turns, which is among the reasons that tires tend to be short lived on a sidecar rig. If the hack and rear wheels are side-by-side, stability is usually too poor to be safe.
I was going to add a note about the difference between wheels with tires that roll on the ground and other wheels that would be used in the car (window mechanisms, lock disks, cams, crankshaft, pulleys, transmission and differential gears, steering wheel, old fashioned radio tuner, alternator and starter parts, etc.), but I wanted to see what the responses would be.
Most cars have 5 wheels, because a car with 4 wheels will sitting by the side of the road if one goes flat. A trike has the same problem if it doesn’t have 4 wheels. I’m not sure how the trend is going, but people don’t like no-spare solutions. Real spares seem to be coming back after a lot of grumbling about hardball spares, and solid core tires just don’t seem to catch on (I don’t know why). But people will pay a premium for auto-inflation and then an even bigger premium when they find out that just one tire can’t be replaced. Go figure.