I think is may be a 1983 Trek 500. Gorgeous Logo on the front
Trek Brochures: https://web.archive.org/web/20240430080616/http://www.vintage-trek.com/TrekBrochures.htm
1983 Brochure: https://web.archive.org/web/20240430080613/https://www.vintage-trek.com/TrekBrochure1983Part1.htm
by drewpul141414