"or was it a tune called Washington Square which featured a banjo solo"

"Washington Square" by the Village Stompers. 1963. Great song as I recall (& I think it was 5-string claw-hammer style banjo).

Also "Sweet City Woman", 1971, by the Stampeders. Won a Juno (Canadian eqivalent of the Grammy) for best single of the year. In my 'memory-replay' I'm hearing a tenor banjo.

Off on a slight tangent, a friend of mine, Alfie Smith performs "Minnie the Moocher" with a 5-string - and makes it work!