The battery voltage is unimportant here. The computers have circuitry that converts the input voltage (19 V) to whatever is needed to charge the battery, and further circuitry to convert the battery voltage down to the 5 V, 3.3V, 1.8 V or whatever the processor runs on.
If one computer is using 14.3 W, that would be just over 0.75 A at 19 V. How did you measure the 14.3 W? If you measured the power taken by the AC adaptor, that will have some losses, so the computer would be taking less, probably 0.65 A
The computers will take very variable amounts of power. If the battery is charging, or the processor is working hard, or the display is bright, then more power will be taken. Start-up can be particularly hard as the processor often runs at full power for a short time.
I don't understand why the AC adaptor has a lower rating. It has to be able to supply no current, or it would fail when plugged into the mains without a computer connected to it, or with the computer turned off.
You should be able to take a 19 V power supply with a large enough current rating, and run all 5 computers from that. It does not matter if your power supply has a larger current rating than the computer, as long as it is 19 V. The power supply produces 19 V, and the computer takes what current it needs. *
It would be good to know what the maximum current is, because the figure of 0.65 A (from the 14.3 W) is a lot less than the 2 A for the car adaptor, which I assume works fine. The power supply figure of 3.42 A might be for larger computers, but I'm not sure, as it could be that 3.42 A is the maximum current if the battery is charging, and the computer is turning on, and the screen is bright.
Without knowing the current more exactly, you could allow for around 10 A for five computers. Here is one possible supply:-
https://www.newark.com/xp-power/ves180ps19/adapter-ac-dc-1-o-p-19v-9-47a/dp/33AH2569
I agree with rjenkinsgb that a fuse for each computer is a good idea.
* There are quite often questions on this forum about whether you can have a supply with too much current rating. Generally, you can't. You are quite OK to plug the power supply for your router into the mains socket, where that mains socket can supply a 1500 W heater. Both the heater and the router power supply are rated at 120 V, and each takes the current it wants. Similarly, a car has an interior light that takes 0.05 A from a car battery that can supply 500 A to crank the engine. That is fine because both the starter and the interior light are designed to run from 12 V.
The only consideration is fusing. If something fails it can take more current than intended. It's then a good idea to have fuses to protect the wiring. If your car's interior light shorted, with no fuse the battery could supply enough current to burn the thin wiring that supplies an interior light. That's why there's likely to be a 5 A fuse somewhere in that circuit. On the other hand, the starter has wires as thick as your finger to take the huge current.