You need 3 AA batteries.
Therefor the sensor should still work at 3V.
If you use a transmitter (switched on once per 5 minutes) it should last for a year.
And lets assign half the current for the sensor.
Suppose AA battery of 1500mAh, I use 1000mAh for safety. One year is 24*365 hours.
Current is 114uA. Half of that is about 60uA.
Perhaps a sensor like the AN48841B or the SL353LT.