On August 15, 1998, at 1620 central daylight time, a Piper PA-28-151, N4576F, operated by a private pilot sustained substantial damage during an overrun on runway 5 (2,050' X 200' dry/turf) at Redwood Falls, Minnesota. The pilot and one passenger reported no injuries. The personal 14 CFR Part 91 flight was operating in visual meteorological conditions. No flight plan was on file. The flight departed Marshall, Minnesota, at 1600. The pilot stated in a written statement that he made three attempts to land on the runway, going around each time. On the fourth attempt he landed, but was unable to stop the airplane on the runway. He stated that a slower approach speed and harder braking would have helped avoid the overrun. An examination of the airplane subsequent to the accident failed to reveal any pre-accident anomalies.