Differential voltage measurement using Arduino
As you do it with the multimeter: connecting ground to the lower potential (4.95 Volts in your example) and the volt probe to the higher potential (in your case 5.0 V), you can also connect the Arduino between the two potentials: Arduino GND to the lower (!) potential and A0, A1, ... or A7 to the higher (!) potential.
As long as you use the correct polarisation and the difference between the potentials is less than VCC of the ADC (5V Arduino ADCs) you should be save.
The resolution of the Arduino might be a problem. I don't know what resolution you need; 5V divided by 1024 is about 5 mV per step.
You might want to provide a reference Voltage at Vin of -let's say- 1 Volt if you need a better resolution. That would improve the resolution to about 1 mV per step. But then the meassured voltage must no exceed the 1 Volt reference voltage.
EDIT (Gerben's comment)
You could use the 1.1V internal reference of the ATMega328P (analogReference(INTERNAL))
And please let me give you a security advice: If the resistence in any part of your meassuring setup is significantly lower than the resistance between the messuring points (e.g you shorten the probe wires), then there is a chance that 90000 A running through this setup. That could burn away your hand, arm or even your life. Amperes kill; not Voltage. I've seen a wrench that was vaporized (ok, melted, ok glowing ;-) ) in a second, when it had fallen between the poles of a car battery (12 V; 300 Amps). An you operate with 90000 Amps. !