Thank you very much for the information. I had previously looked at the "spec" page for the regulator that you suggested however I must have missed the quiescent current spec. I checked again today and did see that the value is shown as 0.2mA max. So that is very useful information.
For my test setup I was powering the 5V regulator with a 9VDC from my bench supply. The 5V output of the regulator was open circuit and it was unloaded. For my application this regulator will only be used to provide the pull up voltage for an interrupt pin out of a Maxim DS1337 RTC. So there should be extremely low current draw from this regulator. For my current measurement test setup I was using a Uni-T UT210E True RMS AC/DC Current Mini Clamp Meter to measure the current from the 9V supply. I should repeat the test and instead use a small series shunt resistance to measure the input current to the regulator. I will do this and let you know what I measure. I think this would be a better and more accurate way to measure the quiescent current draw from the 9V supply to power the regulator.
Thank you very much for your help and time. I will let you know what I measure with the series shunt resistor experiment. Hopefully I get a number closer to the 0.2mA value in the spec.
Have a good rest of your day.