The earliest mass production multi-valve engines were 3-valves because of its simple construction - it needs only a single camshaft to drive both intake valves and the exhaust valve of each cylinder. Today, there are still a few car cars using this cheap but inefficient design, such as Fiat Palio and Mercedes V6 and V8 engines. Mercedes claim to use them because of emissions rather than cost reasons.
4-valve engines
A typical 2-valve engine has just 1/3 combustion chamber head area covered by the valves, but a 4-valve head increases that to more than 50%, hence smoother and quicker breathing. 4-valve design also benefits from a clean and effective combustion, because the spark plug can be placed in the middle.
4 valves are better to be driven by twin-cam, one for intake valves and one for exhaust valves. Some Honda and Mitsubishi models prefer to use sohc, driving the valves via rocker arms like the aforementioned Triumph. This could be a bit cheaper, but introduces more friction and hurts high speed power. Therefore the sportiest Honda and Mitsubishis still use dohc.
5-valve engines
It is arguable that whether 5 valves per cylinder helps raising engine efficiency. Audi claimed it does, but fail to provide evidence to support. In reality its 5V engines are no more powerful and torquey than its German rivals with 4 valves per cylinder.
5-valve design doesn’t guarantee covering more head area than 4-valver.
Nevertheless, if the combustion chamber is in irregular shape like the
picture shown, the valves may cover a larger area. The Ferrari F355 makes
use of this to enhance high-speed breathing. Is there any disadvantage? Yes,
faster breathing also harms low-speed torque if no counter measure is taken.
Therefore it is really more suitable to sports cars.
All existing 5-valve engines have 3 intake valves and 2 exhaust valves per cylinder, still arranged as cross-flow. The exhaust valves are larger, but in terms of total area the intake valves are larger. In the F355, by arranging the outer intake valves opening 10° earlier than the center valve, it gets the swirl needed for better air / fuel mixture, hence more efficient burning and cleaner emission.
The advantage of 5-valve engine is still under question. Only a few car makers used it (VW group, Ferrari and the bankrupted Bugatti), but Formula One cars also no longer favour it. Even the Ferrari F1 cars which was once famous for its 5V engine has switched back to 4-valve design a few years ago.