Help with understanding op amp terminal voltages
The answer is in the fine print of the datasheet. (Note 2 on Page 5 bottom.)


  Note 2: Differential input voltages greater than 1V will cause excessive
  current to flow through the input protection diodes unless limiting
  resistance is used.


This is referenced on Page 2 for ABSOLUTE MAXIMUM


  Differential Input Current (Note 2) ..................... ±10mA


Therefore your solution is to limit input current using a series R on Vin- 


such that the offset voltage from input bias current is negligible yet will not exceed Diff input current when you put such a high voltage (5V when comparing it to -xx mV) 


\$V=I_{in}*Rs\$  where Iin differential must not exceed 10mA or even come close to this.(!)

Iin max = ±450 pA

The internal schematic has ESD protection diodes which you are overdriving with a "voltage source" with no current limit into a high impedance input.



Simple answer shown below.







simulate this circuit &ndash; Schematic created using CircuitLab