The D.C. school system probably will not be able to offer drivers' education for 5,000 students this year because it has no money to finance the $600,000 program and no private benefactor has been found, officials said yesterday.

With classes starting next Tuesday, school officials said they are trying frantically to find some private donor to rescue the program. The officials said they have contacted auto manufacturers, car financing firms and insurance companies, including the Geico Corp., which financed an 11th-hour rescue of the program last year with a one-time $600,000 grant, but this time no help has been forthcoming.

The D.C. school board did not include funding for drivers' education in the school system's 1981-82 budget because "there were other priorities," according to the board's vice president, Bettie G. Benjamin.

She said the board wanted to be sure that no classroom teachers had to be cut, as was the case last year when 400 were laid off, and that there would be sufficient funds for "the more substantive subject areas" like reading and math. The $600,000 needed to finance the drivers' education program is equivalent roughly to the amount needed to pay the salaries of two dozen teachers.

Benjamin said the school board had hoped it could "find an angel" to fund at least part of the drivers' education program in the coming school year.

But with no drivers' education funds available at this late date, "they probably won't have it," said Arthur Hawkins, the system's chief budget officer. He said that the 25 drivers' education teachers will lose their jobs unless they can be reassigned to teach other subjects.

The school board has proposed spending $593,800 for drivers' education in the 1982-83 school year, but final approval is uncertain.

O.M. (Tony) Nicely, Geico's regional vice president, said there is "no way" the company can finance the program this year, but added, "We don't want to wash our hands of it. We are willing to go out and try to sell the program to others."

Nicely said Geico, metropolitan Washington's largest car insurance underwriter, stepped in last year to save the program with the understanding that the school system would figure out a way on its own to fund the program this year.

Most insurance companies offer substantial premium discounts to families with young drivers if the youths have taken a drivers' education course on the theory that such training will help prevent accidents. However, a recent National Highway Traffic Safety Administration study indicated that drivers' education does not prevent or reduce the number of accidents.

Janis Cromer, spokeswoman for Superintendent Floretta D. McKenzie, said drivers' education was a problem McKenzie and her staff, who took office in July, inherited from the system's prior administrations. "It's a question of trying to do what we can at the last minute," Cromer said.

Former acting superintendent James T. Guines, who headed the schools through the end of June, said his staff had worked with D.C. council member Jerry A. Moore (R-At-large) to introduce a bill in the City Council that would earmark $3 from each driver's license and learner's permit sold in the city for drivers' education.

That bill is still in the council's Finance and Revenue Committee, an aide to Moore said. The bill would also increase the driver's license fee from $12 to $15, but the learner's permit fee would remain at $5, the aide said.

School officials have also sought funds from the city's Department of Transportation without success.

Last year, 4,250 public school students took drivers' education as part of their regular school program and 583 private and parochial school students took it in public schools during after-school or Saturday classes.