You can use Ohm's law to calculate the current through that resistor from the voltage drop. From your description there is no doubt where the voltage drop is and no doubt why it is occurring. The resistance is excessive for the current and voltage drop required. This setup does seem like a nasty way to generate 5V. Can you install a switch mode power supply? That would be a much nicer solution. Otherwise at least use an external voltage regulator to drop the supply to a defined level. With a substantial part of the drop occurring at a resistor, the supply to the Arduino's regulator will be all over the place and who knows how close you will be to brown-outs.