Chagrin:
Common mode voltage range of the INA128, for 5V operation, is 1.7V to 3.6V (typical) per the datasheet. What that means is that the output of the amp never goes from 0V to 5V -- it goes from 1.7V to 3.6V. This limited voltage range is typical for OpAmps and InAmps.
I can't see anywhere on the data sheet that says the INA128 range for 5V operation is 1.7V to 3.6V.