The default output is 1v/A. So for 5mA, the output should be .005v. Since the Arduino A/D is 10 bits, using the 5v default analog reference, a 5v signal will give you a raw reading of 1023. A 0.005v signal will give you a raw reading of about 1. Exactly what you are seeing.
To get more resolution at for reading smaller currents, you need to increase the load resistance (default is 10K) and/or use a lower analog reference voltage. Doubling the load resistance will give you twice the resolution. Halving the reference voltage will do the same.
Another option is to go to a higher resolution A/D such as the ADS1115 : http://adafruit.com/products/1085