"5,000 Years of Korean Art," which S. Dillon Ripley, the secretary of the Smithsonian, describes as "the largest and most important exhibit of Korean art ever to tour the United States," will visit Washington next summer.

The 345-item show, which has been touring this country since May, 1979, will open here July 15 at the National Museum of Natural History/Museum of Man.

The treasures to be shown include three gold crowns, two gold girdles, sculptures made of jade and iron, and rare porcelains and paintings, many of them drawn from Korea's state collections. A number of these objects, only recently discovered, are being shown for the first time in the Western world.

The show, which began its two-year American tour in San Francisco at the Asian Art Museum, already has been seen at the Seattle Art Museum, the Art Institute of Chicago and the Cleveland Museum of Art. Now in Boston at the Museum of Fine Arts, it will visit Manhattan's Metropolitan Museum of Art and the Nelson Gallery-Atkins Museum, Kansas City, Mo., before coming to the Smithsonian. It will be here for two months, and is scheduled to close Sept. 15, 1981.