The definitive answer to this question depends on more parameters than what you specified. For example, if you can accomodate wiring your modules with 10AWG cable (5mm²), distributing 5V DC could be acceptable: for a 10m x2 (supply and ground) wire, at 1A, that will amount to 0.12V of drop, which probably won't be a problem. (voltage drop can be easily calculated: there are even some online calculators for this: e.g. https://bluerobotics.com/learn/voltage-drop-calculator)
If you want to use Cat5 cable (practical because it is cheap, and you have multiple wires, so you can use the same cable for both power and data), which is typically 24 AWG, you will obviously have a problem: the drop will be 3.28V at 1A so you'll only have 1.72V left at your device.
But if you use 12V and use DC-DC converters, at say 80% efficiency, that amounts to 520mA on the wire, and the drop will be 1.71V (power loss ~1W). This could be acceptable. If you can parallel multiple wires from the Cat5 bundle, it makes it even easier.
Now, if you distribute 12V AC through AWG24 and use bridges and linear converters, you will need 1A on the cable, the losses and drop will be greater on the cable, but you won't care because it will still be able to regulate 5V at your device side. But the total loss will be huge (7W, for a device that consumes 5W). So you will need a much bigger main supply, which may be a problem. You'll also probalby need a heatsink at each module.
So, here is the design procedure I would follow:
Start by deciding the kind of cable(s) you want to use for power distribution.
Decide on a few reasonable options for power distribution: 5V, 12V, 24V, DC-DC converters or linear regulators on the devices side, etc...
Then for each option:
- deduce the current on the line, then the voltage drop, and the power losses using some online calculator.
- Depending on the number of modules, estimate the main supply needs. You'll see that it may seem much bigger than wat you'd expect. This may have an impact on your decision.
- Find the appropriate solution for the device-side supplies and the main supply. Keep in mind that there are integrated DC-DC solutions available around, which is much easier, and probably cheaper, than making your own (e.g. https://www.digikey.fr/product-detail/fr/cui-inc/P78E05-1000/102-5018-ND/9649654). Those aren't more difficult to use than a linear converter.
- That's a good idea to check the total cost of solution: wires, DC-DC or linear regulators on the devices, main supply.
- You'll also probably want to check what physical size each solution takes, both on the device and the main supply side.
At that point, you'll know what is the best option for you. Here is what you'll probably find out:
- Distributing 5V is probably impossible, or makes the cabling too impractical.
- 12V is probably a good choice, but using DC-DC converters. AC-DC and/or linear regulators at each module will make the solution bigger and more expensive: Each device will be bigger, and the main supply will be much bigger too.