The pilot reported that prior to the cross country flight, which would require approximately 6 gallons of fuel to complete; he had 7 gallons of fuel in the main fuel tank and 5 gallons in the auxiliary tank. The cross country flight was uneventful; about 0.5-miles away from the airport, on the base leg, the airplane’s engine stopped developing power. The pilot reported he was unable to open the auxiliary tank valve in a timely manner before the airplane impacted terrain approximately 100 yards east of the runway. The pilot reported that there were no mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.