I guess the question is rather "How much power can I run the LED at when getting 5 hours from a single AAA?"
Let's say you will run it of an 800 mAh NIMH. That gives you 1.2*800=960mWh of power from the battery. Which means 960/5=192 mW for 5 hours.
You will need a step up converter. Lets say 70% efficiency which gives you 192*70%=134 mW of power to the LED.
If one estimates the LED needing 3.2V at that power it will draw 134/3.2=42mA
What LED? Pick any. No bigger difference between LED at 40 mA than at 350 or 700 mA.
space