The calculation is rather simple:
*For ideal opamps the difference between both input signals (Vin1 and Vin2) is identical to the voltage across R3 (because the voltage between the opamp (+) and (-) terminals is practically zero).
* When the difference between both output voltages is called (Vout1-Vout2) there is a simple voltage division between both differences:
Vin=(Vin1-Vin2)=R3/(R3+R4+R5)*(Vout1-Vout2).
* Thus the gain (Vout1-Vout2)/(Vin1-Vin2)=Vout/Vin=1+(R4+R5)/R3
(as given already by KARNEL in his answer).