On June 14, 2004, about 0945 eastern daylight time, a Gulfstream American AA5B, N4516V, registered to and operated by a private individual, as a Title 14 CFR part 91 personal flight, collided with trees while attempting a go-around at Crystal River, Florida. Visual meteorological conditions prevailed, and an instrument flight rules flight plan was filed. The private-rated pilot and three passengers were not injured, and the airplane incurred substantial damage. The flight originated in Sarasota, Florida, the same day, about 0900. The pilot stated that he was en route to Athens, Georgia, and the airplane was in level cruise flight at 8,000 feet, when all of a sudden the engine started running roughly. He stated that he was unable to maintain altitude, so he declared an emergency with FAA Jacksonville Air Route Traffic Control Center, and was given vectors for Crystal River Airport, Crystal River, Florida. He stated that he flew the subsequent approach to a forced landing with too much speed, and was unable to stop the airplane on the runway. As he was nearing the end of the runway, he stated that he thought he had enough power to execute a go-around, but as he was attempting to do so, he was able to avoid the fence, but collided with some trees. On June 23, 2004, the accident airplane's engine was examined and no compression was noted in the No. 3 cylinder. Further examination revealed that the No. 3 cylinder exhaust valve head was missing and that the cylinder head and top of the piston had incurred mechanical damage. The center electrode of No. 3's upper spark plug showed evidence of physical contact, and was found pushed against the side electrodes. Two pieces of metal appearing to be pieces of the valve head were found in the exhaust system. According to information obtained from the pilot, the engine had accumulated a total of 1,547 total flight hours since overhaul, and 56 flight hours since its last annual inspection, which had been conducted in October 2003.