Catsweat,
After your message yesterday, I went to harriscyclery.com to see what they had. They offer a couple of 5 speed Shimano freewheels that may do you. I think one was 12-22 or so, and they were only about $20. You might want to go look at their 5-speed and Ultra 6 freewheels (slimline to directly replace a 5-speed). Might be an acceptable alternative to a more expensive upgrade.
Regards,
Raymond