Remember this is a bipolar amp with lateral PNP input transistors, they have a bias current that needs to be supplied as well. Bias current may not be the same for each input ( there is a input bias offset current as well as the voltage) and running it off 5V will probably saturate internal transistor nodes, and will give an incorrect output. 5V is a little on the low side, use a higher voltage ( like 15V) or a different opamp that is rail to rail both on input and output.