Yes, as the wire size physically becomes larger so doesits capacity to handle a larger current.
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Wire size is governed by amperage not voltage. Voltage is an insulation factor when talking about wire. Add up the amperage of fixtures you want in the circuit. Once that is found then the size of the wire can be calculated.
Wire is sized by the amperage that it will carry. 5 kW is 5000 watts. The equation to find watts is W = Amps x Volts. The equation to find amps is Amps = Watts/Volts. As you can see a voltage is needed to calculate the amperage. Once the amperage is stated, the wire size can be given for that particular amperage.
Depends upon the voltage. The formula for amperage or (wire size) is Watts / Voltage. If the voltage is 220 volts, then the amperage would be over 400 amps. This would require a large wire size to run it. If it were 440 volts, the amperage would be 1/2 or 200 amps. That would require a smaller wire size. As the voltage goes up, the amperage goes down. At a thousand volts, the amperage would only be 90 amps. A wire gauge or size of a #2 would carry 90 amps for small distances.
A breaker is sized by the wire size. The wire is sized by the amperage. The formula for amperage is I = W/E. Amps = Watts/Volts. As you can see with no voltage stated an answer can not be given.
The question is irrelevant if you don't include the amperage.