Any suggestions for updating the bike?
First off, if it's running a 5 speed rear cassette it's more likely a 70's model Santana, i.e., an antique at this point. Therefore, I'd recommend that you do as little as possible or make sure that whatever you do you keep the original parts around to put back on in the event you decide to sell it. Any upgrades will have a minimal impact on the future resale and could, in fact, reduce it's value if it's in good condition and could possibly be sold to a collector at some point.
I have 9 and 10 speed bar cons laying around.
That's nice, got any extra derailleurs and chain wheels to go with them? Seriously, you'd need to upgrade a lot to bring this tandem up to late 90's specs.
Will I need a new rear wheel if I want to run a 9 speed rear?
Yes... and it will need to be built with a narrow rear tandem hub, e.g., 140mm if it was built after '76 and 130mm if it was pre'76 OR you could cold-set the rear drop-outs to 145mm and use a 145mm hub. But, as already noted, you'll diminish the intrinsic value of the frame to a collector by doing so.