Welcome back to your bike.
Don't buy any aftermarket carb kits. They will bite you in the butt. The brass parts are not made to the original Keihin sizes and specs and you will be fighting to get it running properly because of the poor quality of the parts to save money. I know it hurts the pocket to get such a small box of parts from Honda but if you want to have the least problems with your carbs do not skimp as many have foolheartly have done without asking.
As Sean said clean your carbs first, use an Ultrasonic cleaner to get the best results for cleaning the insides followed up with spray carb cleaner.
Clean all the stock Keihin brass parts including the float valves and inspect the valve tips for wear marks. You may only have fine particles of rust in the float valves from surface rust in the tank (that the tank needs derusting, so empty and inspect the tank for surface rust! Borrow a loaner bore scope from an auto parts store to inspect the inside of the tank)
Clean up the float brass parts with a small brass cleaning brush(non magnetic from a hardware store, put a magnet on the brass!). Check the edges of the float towers for any edges where the float hangs up on(Hondaman goes into this in his book on restoration in
http://forums.sohc4.net/index.php/topic,65293.0.htmlYes drain the oil, as it has sumped from sitting unused and possibly may be deluted from gas leakage into the cylinders past the rings. Does it kick over still? Have you kicked the motor over occasionally while it sat to keep the rings from rusting? Or did you put any oil in the spark plug holes to lube the cylinders yet? If they are stuck, a 50/50 mix of acetone and Marvel Mystery Oil for 3-4 days soaking helps free up the rings, then suck out the excess with a turkey baster and clear tubing or a Mighty Vac type bleeder.(do this before you change the oil)
Battery, get an AGM battery. I bought a Yuasa AGM from my local shop for @$50 here in NH, cheaper than online even. They might have bought it through Parts Unlimited??
John, BenelliSEI has been buying a Weeze(?) AGM and likes them?
Clutch slip, can be from using the wrong oil. Friction modifiers in oil will cause slippage. You want to get Jasco rated oil. Belray EXL 4T Mineral is a good oil for our wet clutch that HondaMan recommends in 20w50 (if you are in hot weather still or will be storing it for the winter until next spring?). I use Shell Rotella 15w40(in my K5 750 and my goldwings for over 250,000 miles combined) for cooler than 65°F weather riding(yes it is Diesel oil with no friction modifiers and works well in our wet clutch motors)
Master cylinder wetness, how old is the brake fluid before you put the bike away 5 years ago?? Did you keep it flushedcand bled every 2 years or less? It might just need flush/bleed if fluid is clear.
Suck out the old brake fluid from the master with a turkey baster/Mighty vac, especially if it is dark color now(should be clear to the bottom!) If the wetness is at the hose bolt, new copper crush washers will stop that leakage. Are the hoses old rubber? Replace them with new hoses, (not used as some think they can cheap out with), to get the best braking power. Then flush and bleed the brake caliper with new bottle of Dot4 racing fluid (higher boiling point)
