Nope. Never seen a C5 in my life (don't look at my avatar whatever you do). They're completely worthless. Send it to me for scrap.
I run all my old stuff at 32/1 with synthetic oil. 40/1 or even 50/1 would be fine with good synthetic oil. I'm just 'old fashioned' and run 32/1 because I always ran that in my dirt bikes. 16/1 is for 30wt motor oil. McCulloch used to advise their customers to run their oil at 40/1 and all other oils (especialy motor oil) at 20/1 in their saws...
Get it running. You'll keep it because it's cool and different. Everybody needs at least one piece of historic Magnesium. Make things easier for yourself though. Drain out whatever stale crap is left in the tank. Refill it about 1/3 of the way with fresh mix. Cap it and slosh the stuff around. Let it sit for a bit. Drain that out. Refill it about 1/4 full. Cap and slosh again. Drain it and refill about 1/2 way with good mix. Cap the sucker and put some good mix in a spray bottle. Open the throttle and choke and spray two or three good spritz's down the throat. Close the choke and pull the rope. Bet she pops and roars for a sec. Do that spritz and pull a few more times....................and she may well keep running on 'er own. You may have to nurse the choke on and off a bit until the diaphragms get to working right again. I've had many old saws easily wake up this way after a long sleep.
If the carb just plain won't cooperate, then you'll need to put a kit in it. RK88-HL for a full kit, or DG5-HL for a diaphragm/gasket kit. If you're replacing the tank-to-carb fuel line, 3/16" ID
automotive rubber
fuel line fits great, and seals the carb box hole well. 3/16" ID Oregon or Tygon line works great for the inner tank line.
Some folks 'round here don't take too kindly to new members starting things off with "what's this saw worth?" or "anybody want to buy this saw" posts right away. Welcome aboard in any case. I think you'll wanna keep that saw once you get it running. They're really not 'worth' big bucks (very common old saw thankfuly), but they are fun to tinker with. I've never paid more than $20 for one, but minty examples can bring more...