I am reading the data sheet here http://www.ti.com/lit/ds/symlink/opa1664.pdf, and it says:
Wide Supply Range: of ±1.5 V to ±18 V, or +3 V to +36 V
Does that mean I can connect V+ to +5V and V- to ground of a typical 5V linear regulator?
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Yes, you can, and the op-amp will be happy, however your circuit may not work unless you bias the inputs appropriately and take the output swing into account.
For example, the inputs must be maintained between 0.5 and 4V with a 5V supply at 25 degrees C (so narrower range over temperature) and the output cannot swing closer to the rails than 600mV (depending, again, on temperature and upon the loading of the output).
It could make sense to bias the inputs near the center of the input common mode range, which is 2.25V.