Infra Red LEDs - Voltage Advice
The only reason you have not vaporized your LEDs is because your AA batteries can't supply so much current. The "maximum 5V" you cite is the maximum reverse voltage these LEDs can before they break. Remember an LED is a diode which allows current in only one direction. 5V is the maximum voltage when you have them installed backwards

The forward voltage in the datasheet is 1.6V - 1.8V. This is, as you say, what you measured.

You should read How can I efficiently drive an LED? which covers most of this.