On August 02, 2005 about 0800 mountain standard time, a Luscombe 8A, N71780, collided with terrain during the landing roll at the Benson Municipal Airport, Benson, Arizona. The owner, who does not hold any Federal Aviation Administration (FAA) certificates (including a student pilot certificate), was operating the airplane under the provisions of 14 CFR Part 91. The owner, the sole occupant, was not injured; the airplane sustained substantial damage. The personal local flight departed Benson about 0630. Visual meteorological conditions prevailed, and a flight plan had not been filed. In a written statement, the owner reported that the purpose of the solo flight was to practice landings in the pursuance of a sport pilot rating. During the landing roll on runway 10, the tail-wheel equipped airplane began to swerve to the left of the runway centerline. The owner maneuvered the airplane to counteract the veer, but there was not enough of the runway surface remaining for him to be able to realign the airplane with the centerline. The airplane continued to the left, departing the runway surface. The right main landing gear impacted a dirt mound and the airplane came to rest on the right wing. The pilot reported no pre-impact mechanical malfunctions or failures with the airplane. The airplane sustained damage to the right wing.