What does the Vout (Output Swing) Indicate for this IC? For example, if I have +/- 5V power rails and as an input to the opamp having a range of 5 V pp from the function generator, will the output voltage of the opamp also have 5Vpp as well? Is this IC a rails to rails IC?

 

Your old datasheet does not show the small input voltage range. Do not use an input voltage range higher than half the supply voltage.

The datasheet shows with your +/-5V supplies, its output is minimum +/-3.4V when its load is 500 ohms or is minimum +/-2.6V when its load is 150 ohms. A graph on the datasheet shows it does not have a rail-to-rail output even with no load.