The student pilot was on a cross-country training flight, landing at her destination, when the airplane porpoised during landing. About 5 miles from the airport, she initiated the descent to traffic pattern attitude. The student pilot stated that due to the late descent, the airplane's airspeed was higher than normal. The airplane touched down and the nose gear dropped. This was followed by a propeller strike on the runway. The airplane porpoised down the runway, incurring additional propeller strikes on the runway, and then came to a stop on a taxiway. During the accident sequence, the firewall buckled. The student pilot stated that there were no mechanical malfunctions with the airplane prior to the accident.