Shiny is dead on: your battery appears to not be holding a charge; the voltage at 5k RPM is normal. Check the electrolyte levels in each cell, adding distilled water to the cells, if it is a flooded battery (ONLY add distilled water, no acid!).
Be sure to use a trickle charger, no more than 1.5 Amps output. If you use a car battery charger, pushing 5+ Amps, it will boil off the electrolyte, damaging the battery by over-charging it. Adding distilled water to any cell will require the battery to be charged. A very good motorcycle trickle charger is the
Battery Tender Jr., This will attempt to charge your battery completely, switching to maintain mode, once the battery is fully charged -- useful for long-term storage, as it adjusts its charge mode (three different modes, microprocessor controlled) to avoid over-charging; exposed plates become damaged (sulfated), leading to failure of the battery. Hooking up your bike after each ride, will top off the battery's charge, which can extend the life of any type of battery (flooded, gel cell, or AGM), by keeping it at an ideal charge level.
Anyway, try a smart trickle charger to top off the battery, first. After it is fully charged, disconnect the charger, wait two hours, and then measure your battery's resting voltage again: if it is less than 12.6 (conventional flooded battery)/12.8 (AGM sealed battery), the battery is going out -- budget for a replacement sooner, rather than later.
For bike electrical stuff, this is the best book I've found so far:
Motorcycle Electrical Systems: Troubleshooting and Repair (Motorbooks Workshop). The author does a very good job explaining electricity, and the bike's electronics, as far as how to troubleshoot problems (discusses/illustrates how to make/use inexpensive tools needed, as well). Check your libraries for copies to borrow (ISBN-10: 0760327165; ISBN-13: 978-0760327166). Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII