Found this site searching on R5 tips.  I loved 2-stroke enduros so much, I decided to go after the ultimate vintage 2-stroke road bike, which happened to be a 72 R5.  It was my covid project and I tore it down to the nuts and bolts and rebuilt it all (as needed).  It was running when I got it, but the oil lines were messed up and one cylinder had been scuffing along with the usual multitude of bad seals.  I had it bored 1st over, new Wossner forged pistons, all new seals, bearings, and crank balanced.  New battery, points, condenser, coils, plugs, wires, carb kits, full cleaning, 2nd gear was out, and replaced that, new clutch disks.  I'd say it's bone stock with the exception of the .25 over forged pistons, K&N filter element (original air box), and hotter EMGO coils.  Here's my problem....

I have never been able to get it balanced to where both cylinders run consistently outside of idle.  I have timed it multiple times, tried all manner of jet combinations up and down from stock values, and air and needle adjustments, and cannot get it to fire evenly across the band.  Both cylinders will idle, one cylinder will run low-mid range, while the other side picks up through wide open.  In a short while, the cylinder that is not firing at the time fouls with gas/oil.  Rinse and repeat.  Any ideas?

The little aluminum EMGO "performance" coils don't have a great reputation.

Can you hook up an inductive timing light and see if it stops flashing when the cylinder dies?  Try it on both sides. 

So the new points and condensers were original Yamaha, or a reputable aftermarket such as Daiichi?

The brassware in carb kits can be awful, so I'd suggest buying new original Mikuni jets (they are still available).

Ok, had one [x crash job] in late "70's & worked in the local Yamy workshop.
So i'm wondering was it running ok before--fixing it?.
First guess is the throttle slides are in opposite carbs which puts them half a turn out & cutaway forward instead of back.
This makes it run crazy rich but if they're both not doing the same thing then that stuffs my theory. Was a common complaint though with owners playing with carbs.
Next thing [or first thing] has the carb Choke interconnecting tube been misplaced & not on the right side carb--or left side depending which side came off when removing carbs.
Choke runs both cylinders from the left carb & if not connected it ends up with a huge open air hole [normally has fuel transferring across with choke operating].
Has the wrong carb bowl been fitted on the wrong carb [bowls swapped over] as only one has the choke jet thingy & choke tube & that would bugger up both sides 'in a way'.
After all that, & if it's the right side playing up, i'd hate to mention 'right crank seal'.
Unlikely--but would be smoking the village out on the right only if that's compromised.
Center crank seal isn't likely to be an issue as never wears as nothing touches unless crank bearing are worn or spinning on the shaft [which i've seen]. Not a rubber seal & just a close fitting  Labyrinth seal.
That's enough for first guesses. Best of luck & loved my R5.
Welcome from NZ too if you're new.
Sorry if it show multiple edits--sorting mistakes.
Link to crank seal for a look.
photos.app.goo.gl/iFW9jCLM1iJ8mctr5

I did the same, rebuilt a 1971 R5 during covid, 
couple thoughts 
​​​​​​ Assume you’ve put some miles on it and it’s not still spitting up all the assembly oil collected in base, the exhausts have removable baffles some of the holes had carboned up on mine . 
 Air box inlet cover on top can restrict air flow . I have to check it to make sure it’s sitting on there correctly. I think there’s a modification involving cutting a piece out of it but I wanted to leave mine stock.
 Don’t get discouraged ! they are a fun motorcycle just need a little sorting out

Have you synced the carb slides ?

Thank you so much, Morley, for reminding me to check the bleedin' obvious! 

I was having similar problems on my own R5.

I had nailed it down to a jiggered pilot jet in my left carb - original issue was not running below about 4k on that pot. I got myself a quite nice replacement carb from the US, fitted it and it did now run on the left pot. However, strange hit and miss symptoms on the right. 

Anyway, after reading your post this morning, it dawned on me that I was so fixated on the pilot jet issue on the left carb that, when I refitted it, I hadn't connected the connecting tube between the two carbs! 

I took it off again, adjusted the float arm (it was leaking a bit of fuel), refitted it again, this time correctly, and, bugger me backwards with a blunt root vegetable, it now runs on both pots. 

All of my carb parts are genuine Mikuni.

Hi -
I have a 72 R5 and DS7, they are so fun!
I had issues with one cylinder running sporadically and it turned out to be a speck of dirt in pilot jets which were already too small IMO (I ended up at #35 for both bikes).  I cannot overstate just how little dirt it takes to screw up the flow thru a pilot jet, whether on these twins or a single enduro
Other issue as Mr. Morley stated was putting the slides in backwards!
Also to synch them I took off inlet boots and got slides to where speed screw just touched and then turned it another 2 turns and then both in equal amounts when adjusting idle with boots and filters back on.
For me the timing was the biggest bitch to set....the back and forth with screw tightening changing setting and being at limit of travel....finally figured it out
I would not use any aftermarket coils, not that I had a bad experience, but because the stock ones work so well.,..as in a kick of two max when cold and they fire up
 

I was having a clutch issue recently on my R5. I got that figured out but am having a similar issue on my LH side running. When it's on, it runs superb. There is an intermittent in out on the LH cylinder. I put new points and checked the LH condenser but no joy. I have some SV650 coils on order to try. The LH coil is the only thing I have left to try.

Timing is spot on with a timing light. The throttle valves are in correctly with the cut at the carb inlet side. I feel like I wasted time with points as it has the same issue after changing. Used Daichi points so no junk.

Is the battery charging ok?