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5.5 mAh/min
I worked out the .015V or 15 mV that you list is 3 counts on the A/D. It is pretty much impossible to have your numbers vary by less than 1 count, so 4.9 mV is expected.
You say that the output changes by 15 mV ... so you've already made sure that the error is not 5 mV several times in a row, it's 15mV a few times.
You saw the same error in the Aref measurement as in the measurement from the sensor. That points to something on your board dragging down the power supply, or to the power supply. The Aref is not changing - staying constant is what it is there for.
Do you have a USB hub with external power that you can use to power the Arduino? The older hubs that I have will put out a solid 500 mA per port ...
Remember to use good wiring techniques, good grounding, and catch all the issues that have bit you before. After that, it's luck as much as skill, experience or perseverance.
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