The pilot reported that, he became disoriented during a day visual flight rules (VFR), cross-country flight. After a nearly five-hour flight in search of his destination airport, he saw an airport and landed. After a brief conversation on the ground with witnesses, he refueled the airplane and departed in search of his original destination airport. Unable to locate his desired airport and five hours later as the day had turned to night, he spotted an airport and initiated an approach to the east. During the night VFR approach, the engine lost power, but the pilot switched fuel tanks and completed an engine restart inflight. However, the airplane did not touch down on airport property. The airplane landed outside of the airport’s southern perimeter fence, near Airport Road and the southeast airport access gate. The airplane impacted the airport’s perimeter fence and sustained substantial damage to the fuselage and the left wing.