The system is 120 and 240 volts. The calcs can be done with both. Attempting to stay at maximum of 3% Vd, 240 volts is 7.2 volts and 120 volts is 3.6. I use 120 volts as the volts dropped is less margin.
Each of the two 120 volt legs together is your 240 volts.
Sure I believe the lights dim trying to start a 5 Ton AC. The issue here is the locked rotor amp draw of a compressor is so high. This high amp draw exasperates the long distance and small wire size.
The utility has size the wire for amperage, and did not take into consideration the distance, and if refrigeration compressors need to start.
The feeder to a refrigeration compressor needs special attention to be large enough to deliver the proper voltage at the very end of the feeder and branch circuit.
Code and standard engineering practices recommend that voltage drop be no more than a total of 5% at the end of a circuit. This allows for 3% max at the end of a feeder, the utility line, and, in your case, 2 % from the service to the AC unit.
This 5% (3% +2%) is flexible. The utility may be under regulations to offer no more the 5% at the end of their line, and then you are responsible for using that voltage to it's best by sizing wire in your system properly.
Look at page 21 of the booklet for my local utility, states they must provide +/-5%. Also, look for Illustration#31, where they list the wire sizes for long distances.
http://www.cmpco.com/MediaLibrary/3/...s/handbook.pdf
I will copy this over at Heating and AC, in hopes that an expert, either HVAC or Northern, sorry if missed someone, I don't keep close watch over there, can help with the LRA amperage levels of a 5 ton unit.
The utility clearly has not provided the sufficient wire size for the amp draw at this distance. You may have had to tell them the load you will connect, or, at least, they should have asked. The issue is you need to prove to the PUC that the utility is not able to provide the required voltage at the end of their feeder, assuming they own and maintain the overhead line.
You should find the requirements issued by your utility, as you will find what they are responsible for providing, and you will find what your responsibilities are.