You do not have to split cases or remove engine and turn over, to turn an improperly installed shifter shaft if you find you are missing 5th gear and make sure you FIRST CONFIRM SHAFT IS IN BACKWARDS by removing left engine cover and peering very carefully at shift shaft end and seeing threads there. Double confirm when you remove clutch as shift shaft is plainly visible there. No tnreads on clutch side, you have some work to do.
I just swapped the shifter shaft end for end as it was installed backwards as noted above (not by me). Beautiful 4 speed CBX but no 5th just neutral. So based on this thread, I swapped it out in the bike by raising bike on centerstand on 6" of wood blocks. Make sure you use 4 straps for safety as you grab the head to swing under the bike. Remove both exhausts.
Remove left cover after draining oil and removing both oil lines. Remove clutch cover and clutch. Remove oil pan and oil pump screen. Remove oil pump suction horn and draw on a mighty reserve of patience. Get a good light and place under bike. You can see shift fork center bolt tnrough an 1-1/4" hole from clutch side. Crawl underneath with a selection of slotted screwdrivers and a dead blow hammer. There were 2 tangs bent over on my bolt. You gotta bend them back so you can get a good 12mm wrench on bolt. Now prior to this shift the bike and turn clutch shaft so it will shift through the gears until you find the gear that will allow tangs on forks to rest in the drum slots without falling out. Loosen bolt and remove it which takes some time. Push out shaft and hold the 3 forks with your other hand. Once fully out, immediately turn it around so internally threaded end is on clutch side. Now slide it back in and use a snap- on or similar 90 deg pick to worry the shaft hole into alignment with bolt with new tab washer. Install bolt good and tight.
Bend tab (s) around bolt head flats. This is the fun part. Use a selection of screwdrivers to slowly painfully bend tabs back over bolt. Now you will need to scrape remnants of oil pump horn off pump and horn and install a new gasket and bolt on the horn.
Now take a break as you have been all scruched under the CBX in the missionary position..ha!
Re- install clutch and cover and left cover. Oh yeah check that all five gears work and neutral is there by operating shifter and turning clutch shaft. Congratulations, you have done the near impossible and I suggest you try throttle cables replacement next or carb overflow tubes without splitting carbs.
This is not for everyone. However it is quite possible and the CBX is waay better as a 5 speed.
That being said make notes in your shop manual that threaded end goes on clutch side unless you are rebuilding a CBX for an enemy.

Now have a refreshing beverage and ride that sucker.
Tony