Joseph Hirshhorn, the art collector who died Monday at the age of 82, left his entire personal collection of works of art to the Smithsonian Institution "for the exclusive use and benefit of the Hirshhorn Museum and Sculpture Garden," according to his will.

Hirshhorn also left a $5-million bequest to the museum, if his residuary estate is large enough to allow it. In addition, he left to the museum his rights to oil royalties from certain lands in Canada. The total value of these rights has not yet been assessed but is said to be "substantial."

Attorneys for the estate deposited the will Thursday with the clerk of the Circuit Court of Collier County, in Naples, Fla., where the Hirshhorns had a winter home. Probate proceedings for the 39-page document have not yet begun. Because no inventory of the estate has been made, there are no estimates of its total value, according to attorneys, although one characterized the amount as "one hell of a lot."

"I don't know exactly how many paintings there are," said an attorney for the estate yesterday, "but he's leaving almost as much art as he's already given the Hirshhorn Museum." Hirshhorn's original gift to the museum included more than 6,000 works of art. He has given additional works since then.

Much of his personal collection is housed in his residences, offices and in storage, and security guards have been posted at these places since his death. The Hirshhorns are known to have purchased well over 2,000 works of art since the original gift to the museum, among them a major painting by Arshile Gorky, purchased in 1979 for $140,000. Among the other works in Hirshhorn's personal collection are major paintings by George Bellows, Georgia O'Keeffe and Roy Lichtenstein, and sculpture by Giacometti, Degas, Picasso, Nadelman and Henry Moore.

In addition to his wife, Olga, and his family, Hirshhorn also named various hospitals and synagogues as beneficiaries.