You can combine a precision instrumentation amplifier (IA) and an inexpensive CMOS op amp to get the best of two worlds—the precision of a bipolar IA and 5V single-supply operation. Using the INA131 gives 50mV max voltage offset, 0.25mV/°C max offset drift, and 110dB min commonmode rejection. How close the output swings to the power supply rail depends on which “rail-to-rail” CMOS op amp you use. With a TI TL2272 you can expect the output to swing within 100mV of the rails