(written from a Production point of view)
Based on a scene not included in any version of Star Trek V: The Final Frontier, the Mount Rushmore National Memorial is a park in the United States of America that pays homage to five of America's most memorable presidents. Four of the people featured on the mountain are real-world presidents: Abraham Lincoln, Theodore Roosevelt, Thomas Jefferson, and George Washington. Sometime prior to the 2280s the head of an African-American female president was added to the monument.
The final cut of the movie did not include the Rushmore reference and instead implied that Chekov and Sulu were exploring Yosemite National Park, where Kirk and the others were camping. The extended scene, had it been completed and included, would have indicated that they were elsewhere when the camera panned out to reveal Mount Rushmore. (A rough, unfinished version of the scene with a production matte – illustrated above – is in the "Special Collector's Edition" of the movie's DVD.)