I owned a Nishiki Semi Pro 10 speed (2 X 5) a long time ago. If this is a similar vintage bike (mid 1970s) it has a freewheel, not a cassette. If this is the original freewheel with 10K miles on it, then it is probably worn enough that putting on a brand new chain may result in problems with gear changes like skipping. When I get a chain with this many miles on it I always add a new cassette at the same time. You can still find 5 speed freewheels online but you will also need a compatible freewheel remover to get the old one off. Most long time bike shops may still have the tool and can remove it for a small fee. You don't need the tool to get the new one on - it just spins into place. Sunrace makes a 5 speed freewheel you can get on eBay for $17 delivered and it is in the usual 14 to 28 tooth configuration likely to be what came on the bike new.
https://www.ebay.com/itm/303797928556