The Airhead 5 speed went thru many changes over the years. Some parts do not swap with out without swapping something else. Since you have a transmission apart be sure the output shaft you use has the groove in front for a snap ring and use the snap ring. Be aware that there is a change in the angle of the helical gears used (March/April 1982) There are three helical gears and the ones on the input and lay shaft are in gear all the time. The one on the output shaft is only in gear in 5th gear.
The updated shift mechanism is considered an improvement by most. It is not cheap in the USA but can be about half our cost if you get it from Moto Bins in England.
If the dogs on any gear are bad it is likely the holes they fit in are distorted also.
Many Web sites to use, Snowbum, Anton Largiader, Duane Ausherman and a few others.
(I'm on my way now to Turkey dinner.)