At 1600 central time, a Cessna 177A lost engine power due to fuel exhaustion and was damaged during the ensuing forced landing. The student pilot/owner was not injured. The pilot said he was departed Hope, Ark., for Sherrill, Ark., with each tank three-quarters full. He was unable to find the airstrip and circled the airfield for an hour looking for it. He ran low on fuel, so he landed in a field, obtained five gallons of gas and directions to the airport, and took off again. He was again unable to find the airstrip and the airplane ran out of fuel.