Hi,
Yes, the LM317 regulator minimum current can be as high as 10ma, not 5ma, but that is over the full temperature range and with highest input-output differential. This fact is not really controversial though because it's written right on the data sheet.
The LM317L however has a min current of 5ma, and can be even lower (2.5ma) if the input voltage is 15v or less.
This means 240 ohms would be ok for the LM317L for any situation, but for the LM317T for example it would have to be 120 ohms.
Of course if in the application there will ALWAYS be some load current, then that could make that resistor work even if it were a higher value. Some caution is advisable here though, because if the load starts up with a lower current than usual it may end up getting a temporary over-voltage until it gets up to speed because when the load current is low and the resistor is not sized correctly the output voltage goes out of regulation and increases until the minimum current level is reached.
The worst case for any of these regulators is with max input-output differential and highest temperature.