Thank you, Jay. I think mine's been here for only about 11 or 12 years, so that answers my question. It could start popping up in the wrong places anytime now.
That calyx does indeed look like mine, but the blooms on that one are lighter and probably smaller, so mine probably is Campsis x tagliabuana 'Madame Galen.' Thanks for the information about invasiveness. I suppose I will have to consider removing it if that does happen, but for now I'll just enjoy the tropical look it provides.
