As demonstrations at the South African Embassy drew the largest number of protesters yet, attorneys for the District dropped charges yesterday against five persons arrested there earlier, saying it would be "untenable" to prosecute them for protesting the "gross injustices" of apartheid.

D.C. Corporation Counsel Inez Reid, in announcing the dropping of the charges, issued a sympathetic statement for the protesters, saying that "no signficant District of Columbia interest would be served" by prosecuting them.

"It would be untenable for the office of the corporation counsel to prosecute these five individuals who demonstrated peaceably to call attention to the gross injustices which result from the South African policy of apartheid," Reid said.

The embassy protest, now in its eighth week, continued yesterday with the arrest of eight demonstrators, including former U.S. attorney general Ramsey Clark; former U.S. representative Robert Drinan, a Catholic priest who now teaches at Georgetown University Law Center, and Goler Butcher, a former Agency for International Development director who teaches at Howard University.

It was "Lawyers' Day" at the demonstration site yesterday, and a crowd estimated by D.C. police at about 750, protesters from law firms and law schools around the city, showed up to lend their support. The group was so large, pickets had to be split into three lines as they marched on both sides of Massachusetts Avenue, a block south of the embassy.

Butcher labeled the white-minority government of South Africa "a pariah among nations," and Father Drinan, wearing a "Lawyers Against Apartheid" button, called on it to "rejoin the family of man."

Clark sharply criticized the Reagan administration's conciliatory "constructive engagement" policy toward South Africa, calling it "a romance with racism, and we all know it."

Since Nov. 21, when the protest began with an embassy sit-in, nearly 600 people have been arrested in demonstrations here and in 14 other cities, according to organizers of the Free South Africa Movement. They have said the number of arrests will increase dramatically this month and into February to coincide with the introduction in Congress of legislation to impose sanctions against South Africa.

In New York, where seven prominent lawyers were arrested yesterday, State Attorney General Robert Abrams read a statement of support for continuing demonstrations there outside the South African consulate and joined other lawyers in a protest march there.

The U.S. attorney's office in December decided not to bring charges against those arrested at the embassy here, saying the "show trials" that would likely result would just "clog" the court system. Those demonstrators had been charged with trespassing or demonstrating within 500 feet of an embassy.

The charges dropped by the D.C. corporation counsel were for crossing police lines, a misdemeanor violation of municipal regulations punishable by a $300 fine. These charges were dropped against Rep. John Conyers Jr. (D-Mich.), William Simons, president of the Washington Teachers Union, and three other labor union leaders, all arrested during protests last month.

Charges against all the New York demonstrators have been dropped swiftly. But in Boston, at least three demonstrators have asked for jury trials stemming from their arrests while demonstrating against a shop selling Krugerrands, the South African gold coin.