Welcome to KZr Conti.
Like was suggested, you should remove and thoroughly clean out the carbs to remove all of the gunk that I'm certain is in them after sitting unused for 5 years.
They probably don't need to be rebuilt (replacing jets, etc.), just a good and thoroughly cleaning
should do it.
Just be certain that you remove any rubber parts on or in the carbs BEFORE spraying any type of cleaner in them or soaking them in a parts cleaner, as carb cleaner and most parts cleaners will literally melt the rubber items. After 5 years, and considering the age of the bike, it might be wise to just get 4 new o-ring or gasket set for them anyway.
While you have the carbs off, this would be a good time to replace the taped-up intake boots (admission pipes) and examine the intake manifolds that fit between the carbs and cylinder head for signs of cracks and general aging/dryness.
As kzwolfsr mentioned,
Z1 Enterprises
is where a large portion of the members here buy their parts from.
They know these old bikes well, have great prices (most times cheaper than a Kawi dealer offers), fast shipping, and their service is top notch!
Be sure to check out the other parts vendors on the
PARTS LINKS
page here on the site. One of them just might be closer to you, which will help keep the shipping cost for parts to you more reasonable.
And before I forget, please be sure to post some pics of your bike when you can, regardless of it's current condition and appearance.....we love bike pics!