What is written on the motor? If it is in fact a 5V motor, it is meant to be connected directly to 5V DC.
And as far as connecting a shunt resistor to measure current is concerned, it's not of any use for a motor of this size (assuming it to be a 5V motor). The current will be extremely small. You will need very high quality and expensive equipment, or an expensive instrumentation amplifier to see such a tiny current, which will most probably be even less if the motor is on no load, which I suppose it would be. Believe me, I've tried. You have to stall the motor to see the tiniest change on a DSO.
In conclusion, no need to think of the current if you apply voltage lesser than or equal to the rated value.