I almost hate giving it to you as I think you were very close. Most just use a calculator and don't even think about what's behind it, just so you know, that's pretty cool
Okay, and now without further ado...
sdrawkcab!
What we want to do is to calculate the wire diameter. Even better, we know if we use all the same numbers the answer should be 12 gauge or 2.053 mm diameter.
Step 4: Voltage drop from Volage Loss where V0 is 400 volts and loss is 3.9%
Voltage drop is 400 x 3.9% / 2 = 7.8V
Step 3: Calculate Resistance for 5 amps
ΔV = I x R, so R = ΔV / I = 7.8 / 5 = 1.56 Ω
Step 2: Calculate Area for 1000'
R = pL ÷ A; p for copper is 1.7 × 10-8 Ω m
Solve for area: A = pL ÷ R;
A = 1.7 × 10-8 Ω m x (1000 feet x 0.3048 meters/foot) ÷
1.56Ω = 3.32e-6 m^2; or 3.32 mm^s