I dont envy you @julian_orteil !
However having seen that picture it LOOKS as if the wires are consistent in length and guage. So if you measure the resistance of one the others should be roughly the same, (lets say 0.12 ohm) and you can make a correction;
that will involve
ADDING the "constant value" to the 10 ohm resistance to the "+5V" supply, so
const int KNOWN_RESISTANCE = 10;
would become
const float KNOWN_RESISTANCE = 10.0;
const float rWire = 0.12; // measured value for the resistance of a "typical" connecting wire
.. and in setup:
KNOWN_RESISTANCE = KNOWN_RESISTANCE + rWire;
// Calculate the resistance from voltage (using ohms law)
float knownCurrentmO = (POWER_SUPPLY_VOLTAGE_MV - voltage) / KNOWN_RESISTANCE;
float resistance = voltage / knownCurrentmO; // Convert to ohms from mV/mA
resistance = resistance - rWire; //correct for wire resistance
Serial.println(resistance);
Looking at the picture I can see so many "beginner" mistakes. This is very much a protoype, testing design ideas, and not to be used long term, so I hope you dont need to maintain it.
Others have often suggested in threads that the OP should provide a picture, and this has made me realise why that is important. if the OP does not know what to include in a schematic (like in this case the resistance of the wires) the schematic will never properly represent the whole circuit.
Hope this helps.
BTW thanks for the refs to my site, I'd be interested in your feedback if you have time to message me?