You say you are in Seattle, Bob, how many of their bike shops have you visited
with this question and the project with you?
blind guess , buy a new 5 speed freewheel and a new chain
and forget index shifting.
friction /ratchet thumb-shifters, a new pair, china made, are cheap.
I have a 6 that is the same width as the 5
aka Ultra 6, suntour narrow cog spacing, regular 6 is 5+1 at standard space
Suntour is gone for decades now.
only if your hoard is new-old-stock, will a chain mesh well on them
as the wear will mess up the interface of chain and cog tooth.
hence the sugg to buy new.