What is an example of using a stub on a ham antenna, its real purpose
and how it does it?

Hi, A stub used on a ham antenna is generally a "matching" stub. It is a
section of transmission line that exhibits capacitive or inductive reactance
depending on the length and termination of the line. (open or short). Used to
transform a complex antenna impedance to the feedline characteristic impedance.
It may or not require other devices to realize a successful impedance
transformation.
I don't know what an R5 is, on beams, a hairpin match (stub) is often used
for impedance matching.
73 Gary N4AST