At such a low forward current, the voltage across the LED will be lower than nominal, but still not insignificant. If you have voltmeter that can do high impedance (>G ohm) voltage measurements at 5 V then measure the voltage across the 10 M resistor and calculate current. many bench meters should be able to do this, but very few handhelds. Alternatively, if your meter tops out at cay 2 V for the high impedance measurements, then you could measure the voltage across the LED, then calculate the voltage across the resistor, then calculate current.