Vladimir Slepak, who for eight years sought to emigrate to Israel, was convicted of malicious hooliganism in a closed trial yesterday and sentenced to five years' exile in a remote region of Soviet Union.

His struggle to obtain an exit visa has attracted wide attention abroad, including the first personal message of support Jimmy Carter sent to a Soviet dissident. Partly as a result of the notoriety, Slepak has emerged as a focal point of much of the Jewish activism both here and in the West.

The 50-year-old Slepak also was one of the founding members of the unofficial Helsinki committee in Moscow, a group attempting to monitor Soviet compliance with the human rights provisions of the 1975 Helsinki accord.

The prolonged plight of the Slepak family was publicly singled out by Carter as an example of human rights violations in the Soviet Union. On Oct. 21, 1976, Carter sent the following telegram to Slepak:

"I have read with great interest about the treatment you and some of your colleagues suffered recently. As you know, I have spoken out on this matter as governor and during this campaign and have referred to your case by name. I want you to know of my deep personal interest in the treatment that you and your colleagues receive."

But last week, when President Carter was asked at a news conference about his reaction to the June 1 arrest of Slepak and his wife, the president restated his general position without mentioning Slepak by name or addressing the specific issue of his arrest.

Another Jewish activist, Ida Nudel, was also tried and convicted yesterday in a separate court on charges of malicious hooliganism and sentenced to four years internal exile.

It was not announced where the Slepaks and Nudel would be sent. Normally those convicted are sent to small, isolated hamlets in Siberia.

[ Washington, the State Department termed the sentences "unduly harsh and clearly incompatible with the letter and spirit of the Helsinki accord.]

Observers here noted that both Slepak and Nudel could have received up to five years in prison on the charge. Hence yesterday's sentences, while not signaling any change in the Kremlin's crackdown on dissent, may nevertheless he seen as reflecting Moscow's intention to soften its image on the issue. Last month there was considerable international outcry over the maximum sentence of seven years in prison and five of internal exile handed down last month against Yuri Orlov, another key dissident figure.

Slepak and his wife, Maria, were arrested when they held up a large placard on the balcony of their apartment overlooking busy Gorky Street, the city's most fashionable shopping area a few blocks from the Kremlin. It took police more than an hour to break into the apartment and arrest the two.

Since the jailing last year of such key dissidents as Orlov, Alexander Ginzburg and Anatoli Scharansky, Slepak, an electronics engineer, has moved to the forefront of the struggling human rights movement here, contacting Western journalists about activists' press conferences and sometimes acting as an interpreter.

He himself is the son of an ardent Bolshevik who returned to Russia from the United States to fight for the Reds in the Civil War after the Revolution. Angered by his son's criticism of the regime, the father has disowned the son whom he named for Vladimir Lenin.

The trials of Ginzburg and Scharansky are expected to be held this summer. Arina Ginzburg said yesterday her husband is ill and she presumes this is the reason his trial in Kaluga on charges of anti-Soviet propaganda has not yet begun. Scharansky reportedly faces the capital crime of treason. The Soviets have accused him of having connections with the Central Intelligence Agency, a charge which Carter has personally denied.

Nudel, a 47-year-old economist, held a demonstration similar to the Slepaks' at her apartment in another part of Moscow the same day. She, too, was arrested but not held in pretrial detention. Mrs. Slepak, a 51-year-old physician, was arrested with her husband but later released and sent to a hospital for treatment of pancreatitis. She is still hospitalized and is to be tried later.

One of the couple's sons, Alexander, 26, emigrated to Israel last year. Another, Leonid, who also has applied to emigrate to Israel, has been in hiding since last November when he received a draft notice.

Yesterday's trials were barred to Western correspondents and representative of the U.S. Embassy, First Secretary Raymond Smith, as well as to friends of the two defendants.

Nudel, being tried in a court in the Volgogradsky district of the city, refused to enter the courtroom without her friends. But she was eventually taken forcibly by police and plain-clothesmen into the courtroom at the order of the presiding judge.

As Slepak was taken away by police following the trial, someone in the courthouse grounds turned a high-pressure hose on reporters and dissidents talking outside the building. The group was soaked but no one was hurt.

The official Soviet news agency Tass aid after Slepak's arrest that he had "zealously" violated public order during the placard protest, which was witnessed by several hundred Russians and some tourists who gathered below.