I disagree that the five-string banjo came to America via Ireland. There were plenty of touring companies of Uncle Tom's Cabin throughout the US in the time of the minstrel show which employed the minstrel style banjo which is close to the tradition of Uncle Dave Macon, Stringbean and Brother Oswald on the Grand Ol' Opry. The Irish tradition of the banjo was not the five-string banjo but the tenor banjo which is closer to the Irish bouzouki or dropped-tuned mandolas. You rarely hear this type of banjo playing in American Appalachian music. Cammemeyer came out with an English five-string with a channeled fifth string through the head of the instrument in lieu of the fifth peg. I don't find this in Irish music, however. This was used in the early nineteen hundreds when there was a classical banjo craze by the likes of Fred Van Eps and Vess Ossman.

It is conceivable that the minstrel banjo of a four-string variety found its way to Ireland through folks like Barney McKenna. I have heard a few selections of chordal tenor style employed in Ceili bands from local American branches of the Comhaltas. Mostly, the banjo style is single-string picking the "chune" with the other instruments.

Appalachian banjo styles definitely come from the minstrel show tradition which is basically stage banjo entertainers using the style of early slave musicians. The banjo was not as popular on the plantations as was the fiddle, however. The minstrel show was responsible for the popularization of the five-string banjo in Appalachia.