Ask an American teen-ager what he knows about Korea, and he'll probably tell you what he's learned watching "M*A*S*H" on television. Ask his parents what they know, and they'll tell you what they learned from the first run: the muddy, bloody Korean War.

Either way, the image of this venerable, ancient land is one of the present Korean Ministry of Culture would like to change, so they've now mounted their own peace offensive on the "M*A*S*H" generation: "5,000 Years of Korean Art," an exhibition that incudes 345 dazzling works -- shimmering golden crowns, exquisitely wroght gold and jade jewelry, celadon-glazed ceramics that rival the most beautiful ever produced, Buddhas and genre paintings of warmth and charm. They are the national treasures of Korea, the greatest works their artists and craftsmen have ever produced.

The show opens today at the Smithsonian's National Museum of Natural History/National Museum of Man in the new Thomas Mellon Evans Gallery. It begins by pointing out that despite its strategic location on a peninsula between China and Japan, and the ceaseless, bloody foreign invasions that resulted, Korea has managed -- miraculously -- to remain a cultural entity unto itself, albeit overshadowed by its neighboring giants. It is the goal of this exhibition to establish that there is a separate Korean identity, and to point up its distinctive character -- in essence, the spirit of the Korean people. It is here for the seeing in the kind of show that reaffirms the notion that art, in the end, may be the greatest peacemaker of all.

Back in 1958, an earlier exhibition of art treasures from Korea came to the United States, but fell flat, partly because of lingering bitterness about the war, and partly because of a general lack of interest in oriental art. Since then, Americans have become far more sophisticated in their tastes, thanks in part to a succession of blockbuster exhibitions that have sharpened both their eyes and their appreciation of what had happened over the centuries in parts of the world beyond Paris, Florence and New York. In the early 1970s in Korea, meanwhile, several archeological treasure troves began to be discovered, revealing works that are unique both in Far Eastern art and in the world. These revelations alone make this exhibition worth seeing.

Though it starts with some very eary, elegantly shaped black pottery from 3000 B.C., daggers and early bronzes, the eye-dazzlers here are the gold crowns and metalwork from the 5th-and 6th-century royal burial sites of the Old Silla Kingdom (57 B.C. to 668 A.D.). Unknown elsewhere in the Far East, these crowns consist of diadems of gold topped by protrusions shaped like trees and antlers and festooned with small, comma-shaped bits of jade and glass, and tiny circles cut from sheet gold. Five such crowns have been found in Korea, and three are here, all believed to be derived from prototypes used by the shamans of the Siberian steppes, who wore real antlers on their heads. These crowns, when worn must have shimmered like aspen leaves. This distinctive effect was obviously also sought -- and attained -- in the exquisitely worked beaded filigree necklaces, earrings and bracelets found in these tombs, and without parallel in Chinese and Japanese art.

The tombs also revealed some extraordinary early vessels for holding liquids, all of which look like bronze, but are, in fact, made in unglazed gray stoneward. One, for example, is a 6th-century vessel shaped like a warrior on horseback, the soldier overburdened by his elaborate war regalia, and the poor horse overburdened by them both. This tendency toward a kind of homey, informal humor is an endearing characteristic that persists throughtout Korean art, even in the gold, bronze and iron Buddhas, which seem somehow more approachable, more human, than the idealized Chinese prototypes.

The 12th-century celadon porcelains from the Koryo Kingdom are the one aspect of Korean art that has been long appreciated, even in Japan, where they were collected -- along with the potters who made them -- as early as the 16th century. These luscious bowls and melon-shaped teapots -- incised, carved forms with lustrous, graygreen glazes -- reassert their status among the world's highest achievements in clay.

The elaborately inlaid celadons, epitomized in the famous 12th-century "Thosand Cranes Vase" on view here, are a uniquely Korean contribution to this art. But also typically Korean are two waterdroppers made of celadon -- small hand-held accessories for a scholar's desk, used to moisten an ink block. One, a "Monkey-and-Baby"-shaped dropper in a tender madonna-and-child-like configuration, is pure sentimental kitsch in any age. Similarly loving depictions of animals turn up often in the paintings, too, including one of a dog unceremoniously scratching himself, and another of playful cats scrambling up a tree in pursuit of several sparrows. Even the striking 18th-century painting of a coiled tiger, who threatens to burst from the confines of his silk scroll, seems to hae a pussycat face. Tigers were plentiful in Korea until the 20th century, and were worshipped for their strength, and possibly drawn from life. The lifelife rendering is also a distinctive quality of the several genre paintings and portraits on view.

The show was amply and approachably installed by Beth Miles, who also designed this new exhibition space, the sorely needed half-million-dollar gift of Thomas Mellon Evans, whose colt, Pleasant Colony, won the Kentucy Derby and the Preakness this year. The Washington Korean-American community raised $8,000 for the publication of a fine free brochure that accompanies the show.

Nearby, in the Learning Center, the Smithsonian has installed a small exhibition of contemporary work by the Washington Korean Artists Association, proving that their art traditions continue to flourish here. For those who want to explore further the more subtle differences among Korean art, Chinese prototypes and Japanese derivations, the Freer has mounted a small show of 40 exquisite examples of its own Korean treasures, in close proximity to galleries showing Chinese and Japanese work.

The Smithsonian showing is the final stop on an American tour that began at the Asian Art Museum of San Francisco in May 1979. Though the original plans did not include a Washington stop, the new Thomas M. Evans Gallery made it possible by giving the Smithsonian, for the first time, a decent hall in which to host major loan exhibitions.