Shifting -5 V to +5 V signal to 0 to +5 V for ADC
The 741 can't accept an input that's too close to the negative rail. The data sheet says the input range is +/- 13V when the power supply is +/- 15V.  Not sure about when the negative power supply is 0V but I doubt it will work the way you expect with a 0V input. Similar story on the output side. That would explain the strange numbers you're getting below -4V input. Don't know what's going on with the +4V input since there would seem to be plenty of headroom with your +12V supply. Does the simulation work if you power the 741 with +/- 15V? It looks basically correct if you assume that the op amp is ideal.