Operational Amplifier Circuit - +/- Signal to 0 ... 5 V
Starting with the op-amp, the TL081 recommended supply voltages are +/- 5 volts to +/- 15 volts so it fails the first test because you are using a single rail supply of only 5 volts.

If it were an op-amp that could work from a single supply of 5 volt you hit the next problem of the quiescent output signal being set at 0 volts for equal values on the input. In other words, when using a single rail circuit like this you need to bias the op-amp via R7 to possible mid-rail (2.5 volts). 

Putting all the above to one side, if you used a 5 volt rated rail-to-rail op-amp then it stands a chance but you have very low values for R11 and R12 and more-than-likely, any op-amp you choose won't be able to supply the current just to get the bias condicitons right.

I would also scale up R4, R5, R6 and R7 by a factor of ten to avoid the op-amp having to supply 10 mA to the feedback network when the input differential is 10 mV.