Query approved

What is the capacity & type of battery you are using in that bike ? You should be using the older flooded lead-acid type only on this bike .
12.7 is just the correct fully charged open-circuit voltage of this battery type ( at around 28C removed from the charging source and kept for an hour) . So your battery seems well charged now . The RR units made for these old bikes were rather crude .. Max charging voltage should be around 14v when you measure the terminals with battery connected and rev the engine, so the charging voltage you are getting now is a bit low . Also it should not go down to 5v at any point , even with load ... that would deplete the battery fasssst . That yours does get to 5v while revving the engine, indicates a problem ... may be even a short somewhere in the alternator coils , points system, wiring harness etc . At 13.5 volts , which is nearer to the trickle-charging voltage of this battery type , it would take hours n hours to get it to full juice , days even if it was full flat ( around 11.5) to begin with . Also before you start to trust a new meter, calibrate it against quite a few known stable voltage sources to have a gauge of it's accuracy . I don't believe a new RR unit for this bike ( of the same type as OEM) would be any better . You can consider alternate RR units from other bikes/vehicles (like the APE) .
ps- I used to have a roadking once , and battery charging sucked on that one too .. never found a solution other than to have it recharged externally every month or less .

Dont worry brothers.... please fit 6amps diode from lighting line to battery positive... it will give average charging for citi riding