At this point I would suggest you stop what you're doing and visit the KZ1300FAQ tab at the top of the page. There is a wealth of information there and what I think is important here is that there are a number of common issues that these bikes have that really need to be looked at before continuing on operating a bike that you have no history on and a lot of that info is talked about in the FAQ's.
If I had bought that bike you just got and I found water in the oil and the fuse block with copper jumper wires in place, I would have assumed that the previous owner was a butcher and shouldn't have been allowed to operate a 3 speed bicycle. I'll assume that water in the oil was the straw that broke the camel's back and that's why he put it on the market.
Regarding #4 and #5 dead cylinders- there's nothing common between them. #3 and #4 share an ignition coil, so if #3 is running then #4 being dead is probably a fuel issue. Same with #5. It shares a spark with #2 so if #2 is running, again #5 is probably a fuel issue. You're likely needing to pull the carbs and overhaul them.
The carburetors on the KZ1300 are Mikuni BSW32's and the Idle/ transition circuit is very sensitive to debris clogging. 80% of the discussions on this site pertain to that particular problem and there's a wealth of info on how to "properly" fix the issue in literally 100's of posts on this site.
Also, before you go any further, please find the information in the Frequently asked Questions tab regarding the cam chain tensioner and inspect the tensioner plus the idler roller and the tensioning roller. Far too many members have had to rebuild the top end because the cam chain jumped a tooth and bent a valve.
This should point you in the right direction and get you going. We're here to help when you need guidance.
I have looked at the tutorial on how to clean the carburetors, I have removed them from the motorcycle, also what is left of the airbox to clean it.
I started with the easiest thing, disassembling the cups and seeing what was inside.
One carburetor came out clean, the one on cylinders 1 and 2.
The central carburetor, cylinders 3 and 4, came out with dirt inside, the glyceurs were clogged, I washed them with dichlor after removing them from their housing, with a syringe I sprayed dichlor from the ventury holes until liquid came out fluidly.
I have repeated the operation with carburetor number 3.
The duct that supplies fuel at idle in carburetors 2 and 3 was also clogged, my lips are still swollen from contact with the dichloro when blowing to unclog them.
After reassembling everything, I remounted the carburetors on the bike and tried starting it.
Its roar and softness has given me a chill.
Now all cylinders are firing.
The problem has been that the exhaust system mufflers have the inner fiber with traces of oil and it has started to smoke when it has started to warm up, I have had to stop at the risk of the fire alarm in my garage going off.
When I receive more pieces to complete the puzzle I will do a dynamic road test to burn the remains of oil from the exhaust.
To be continue...