I have a 24-48V power supply and opamp that i want to use is lmp8601 which takes +5V-GND power supply and can take common mode voltage upto 60V. Problem here is that I do not want to use two separate power supplies. I wanted to know if the opamp will work until the difference between postive and negative rails is 5V i.e if I give let's say 40V to +Vs and 35V to -Vs, will the opamp still work or is there any limitation for that?
The maximum supply voltage of the LMP8601 is 6V so indeed you cannot use the 24-48 V supply. As long as you make sure the opamp's supply voltage does not exceed 6V it will work. So yes you can feed it with 40 - 35 V = 5V as long as you make sure that the input voltage remains within spec.
The input voltage range is -22 - + 60 V but that is relative to the -Vs pin of the opamp ! So if you feed it with 35 V and 40 V then the lowest input voltage allowed is 35 V - 22 V = 13 V ! Also note that the output voltage of the opamp will then also be relative to 35 V since this will be the "ground" from the opamp's view. So the opamp's output voltage will always be between 35 V and 40 V.
But why not feed the opamp with +5 V and ground ? Just make a local supply voltage using a regulator or a resistor and a zener diode ?