Replacement vintage Raleigh chain I'm refurbishing a 1988 Raleight winner with an original worn chain. It has a 5 speed rear freewheel and a 2 cog crank. Advise please on which chain I need and where to purchase.
You need a standard 3/16" wide 5 speed chain.  They're relatively uncommon now-days, so you may end up with a 6-7-8 speed chain which should be adequate.

Downside is fitting a new chain to a worn cassette/freewheel will probably run even worse.  Do consider fitting a new freehub too.

Lastly, check the front chainrings for wear.  If the teeth are worn-looking then consider a hat-trick and replace all three.

At this point you might be looking at more cost than the bike is worth, at least as far as new parts go.  You'll have to make a call if its financially worth doing.