Thought I'd see if some of the great Enduro minds here could give me some ideas. The bike is running great, idles at 1500 RPM, and it'll wind up to 6500+ RPM in every gear except 5th. Once I'm in fifth gear, as soon as I approach 5500 RPM it's like a governor kicks in and it won't go any faster.

 A neighbor suggested maybe the 50-year old coil wire, so I found some replacement coil wire at O'Reilly's, and tried that, but it's exactly the same. Seems so strange, because it runs beautifully in all the other gears, but just levels out at 5500 in 5th.

Does it need a new coil? New points, wider points gap, smaller gap? I tried both spark plugs and they are gapped at the recommendation, and they both have the exact same result.. 

Welcome. Are you just expecting too much from the poor old thing. Is the gearing super high like top gear is an overdrive & just can't pull it any faster. If ya talking trail gearing & you feel it should tap right out, then does the exhaust need a burn out. Points need a reasonable gasp to get the timing near 1.8mm btdc but no more than a tight nipping 15thou on the feeler blade through the flywheel slot. Not sure what mine revs too [if you can believe what it says] but i've got a video on here somewhere to compare or sort of get a bit of an idea. Mine though is a ratty old AT1-125 with a 175 reed inlet top end.

Found the video. I should be shot at dawn for a week reving the snot out of it like that. She's a willing rever though [my excuse] Have a cotton reel very small sprocket on the back [100mph gearing--in my dreams].

I appreciate the response, but it actually kind of sputters as it tries to go over 5500 RPM, ONLY in 5th gear, and then it stays at 5500 even if I increase the throttle. I rode one of these back in high school and I know that it'll rev up higher and go faster in 5th gear. It has the stock 16/45 sprockets. By the way I'm riding on level streets, with no headwind. I also weigh almost exactly the same now as I used to in high school. I just reduced the gap on one of the spark plugs down to .020, and I'll try that out tomorrow.

I'm reticent to play around with the points, because it seems to start up and idle perfectly, and it runs great in every other gear except 5th, when I get up to 5500 RPM.

 By the way I'm not sure what people mean by the burning out the exhaust. I removed the 2 parts at the end of the exhaust and cleaned all that up, and it seems to be clear inside. The bike only had 340 miles on it when I began working on it.

340 original miles?, that's a lucky find, so yeah exhaust should be good at that milleage. Exhaust in the partzilla link shows two parts & i'm guessing the spark arrestor is built in down in the long part & should be visible looking in the end with a torch. They get restricted in that part. But at that milleage its totaly unlikely. Compression feels good & bouncy? on the kickstart. Air filter not falling to bits with age. In the Carb there's an important little Oring to seal the needle jet into the bowl so the main jet doesn't get bypassed in which case it'll go all rich. But if its pulling good revs in the lower gears it shouldn't be that. Points gap [more gap more advance timing] you can eyeball through the slot just moving the flywheel back & forth over the opening & forward a bit then back to close & get good at guessing 14-15 though & 12 just looks close. So after all the--i'm no use lol. ps, we love pics.
Just to add--my thoughts--if it's not missfiring i doubt its electrical related--unless retarded timing [close almost invisible points gap] of course but that'll only knock the overall performance & top end not missfire as such.

I've been posting here for a month or so, in other threads, primarily "registering a bike after 30 years". This bike was purchased by my dad, who also bought me one back in 1971. I just recently spent a month restoring it. Not doing a full cosmetic restoral, but cleaning out the fuel tank and carburetor, getting the engine running, installing new crankshaft seals, and repainting a couple of the parts that were super rusted, mainly the chain guard and the rear fender. In the past several days I finally got new tires and brake shoes on it, so I've been testing it at higher speeds.

The old petcock for the gas tank was shot, so I ordered one that has the same bolt pattern for a Big Bear ATV and some other current Yamaha products. However it only has a 1/4" outlet, and the original was 5/16". I adapted it with a large fuel filter, using only an inch of quarter inch fuel line, then going back up to 5/16 fuel line down to the carburetor. I'm wondering if that might be part of the problem?

However, it just seems so strange that it'll wind up just fine in every gear but 5th. It hits 5,500 RPM, then begins sputtering, and just will not go past that, only in 5th gear.

 I did look at the points as I rotated the flywheel, they seem to be opening and closing at about the right gap from what I remember when I used to work on these. The stator was also very clean.

Na, fuel tap should be good as bigger than the main jet by plenty & keeps a big bear 350/400 running, 4 stroke admitedly--but!!. I'm out of usefull ideas without riding it. Not leaning forward into the wind & pushing the rear brake on. Ok i'll stop being stupid.

I agree, I think the quarter inch petcock should be fine. These things get 120 miles per gallon, they aren't sucking down fuel that fast. My neighbor, who works on vintage motorcycles and cars a lot, was really focused on the coil, the coil wire, and possibly replacing the points. He said when it gets into 5th gear, there's more of a load on it, and that's going to stress the ignition. That's why my first fix was to replace the coil wire to the spark plug, and I guess tomorrow I'll look into testing the coil, after I ride it with the spark plug gap reduced, which is another thing he suggested.

"By the way I'm not sure what people mean by the burning out the exhaust." 

Those folks that have the space will light a bonfire, barbie etc and put the exhaust on the fire, so that all the built up carbon, unburnt oil etc will burn off.

Years ago, the exhaust on a DT125 that I owned had to be sawn in half to get rid of all the crud. It was then welded back together, re-painted and ran fine.  

Be great if you could do a video sometime so we can hear how it goes & revs etc. Not easy i know. Think i was holding the camera in left hand then paddled off & popped in gear, then go for it. Messy video that it is.