stephen, not only instamp but also adc has its own noise,
you have to take care of 2 things,
1. offset voltage error
2. common CMMR
if you look at 5uV is high noise, i addvise you to use external instamp like ad623, and also be careful about adc,
if you are working on a signal at about F hz, than sample it minumum 2Fhz (much is better) than apply moving avarege filter,
it wil give you the average noise of the system, the remove this noise to the every sample you get,
it is not the best solition but it works in high frequency.
