Is there an amplifier voltage limit for the input signal even if the differential voltage is small?
As shown your circuit will not work.  You state that the common mode input range of the amplifier is 5V, yet you have the inputs tied to a shunt on a 24V output.

You could try to build a precision divider on the input to the amplifier, but a simpler solution is to get an amplifier more suited to the task.  There are lots of current shunt monitor products that can operate with a 24V common mode input.  Here's one example from TI, but you can find others from TI or Maxim or LT etc.

INA303