To calculate the common log of 5, key 5 [LOG], where [LOG] means "press the LOG key".
To calculate the natural log of 5, key 5 [LN].
These menu keys are in the [MATH] [LOGS] menu, of course.
Almost all the "scientific functions" are used this way in both RPN and ALG modes, namely, they act immediately upon the number in the display. Almost all old calculators worked this way, unlike modern ones on which you press [LOG] 5.
FYI, the HP 19BII Owner's Manual covers logs on pages 50 and 51, with an example on page 51.
Disclaimer: I don't work for HP, but I enjoy using their calculators.