I ended up putting on fresh brake cables and replacing the left shifter cable. The unique Sprite shifter on the top tube uses a unique cable. The disc head of the cable is larger than a derailleur cable head but smaller than a brake cable head.
To make a cable, I took a standard disc headed brake cable and ground the disc down to size.
I also re-greased and reset the bearings on the S-5 hub. The result is a better functioning Sprite.
If you've ever wondered what a "high performance" Raleigh Sports would be, the Sprite with S5 hub is basically what you would have. It's a fun bike with a little more range and gearing flexibility than a Sports, but it still rides and handles like a Sports.
This is an enjoyable bike, even if the shifting is a bit more complicated than a 3-speed.
The simple "Sprite" logo on the down tube is very plain compared to some of the other types that have a number "5" printed over them.
I also added fresh handgrips (Kenda brand Dare knock-offs) and cleaned up the Duro white walls. This bike originally came with Dunlop "White Sprite" white walls tires. I added the Duro tires a couple of years ago, but they have few miles on them. It's a fun, lively bike.