There is no single conductor that will handle 1500 amps. For ease of handling, the conductors should be installed in parallel, triple or quad runs.
For a parallel run, 2 - 2000 MCM with an insulation factor of 90 degrees C will give you a total ampacity of 1550 amps.
For a triple run, 3 - 750 MCM with an insulation factor of 90 degrees C will give you a total ampacity of 1500 amps.
For a quad run, 4 - 500 with an insulation factor of 90 degrees C will give you a total ampacity of 1580 amps.
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As a service entrance wire you need AWG # 3/0 gauge copper.
AWG 10.
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.
# 4 copper wire short distance.
The V stands for volts and A is amps. If for example you have a 12kVA device and are running off a voltage of 120 volts then Amps = 12000/120 = 100. You then use the calculated amps in a wire size table to get the correct size.