smhall05:
input impedance of 1 M OHM (DC), this explains why I am falsely seeing this drop.
The drop you are seeing isn't false. It is very real and correct.
smhall05:
If the input impedance was say greater than 10Meg, which is the case with better voltmeters I would have seen what I expected, 5.09V.
No, you would have seen 5.03V, not 5.09.