The Reagan administration started firing striking air traffic controllers yesterday and federal judges put five of their number behind bars, but the union appeared to be holding firm in the third day of its nationwide strike.

Seven-day dismissal notices went out to controllers on the East Coast at 3 p.m. yesterday, four hours after the administration had originally scheduled the firings.

White House officials said yesterday that the delay in issuing the notices was a result of "technical problems," and not of any weakening of the administration's determination to break the illegal strike. Reagan aides said the president's original 11 a.m. work-or-be-fired deadline yesterday was set inaccurately Monday morning. "It was stated the wrong way because it really didn't take into consideration that the first controller shift after 11 a.m. begins at 3 [p.m.]," one aide said.

Dismissal notices were sent to controllers who failed to show up for work after 3 p.m. in their respective time zones, the aide said.

"I'm sorry, and I'm sorry for the," President Reagan said of the dismissals. "I certainly take no joy out of this."

While the notices were being put in the mail, striking controllers and their families met across the nation for rallies sometimes interrupted by federal marshals seeking to serve union leaders and members with court orders against the strike.

Five leaders of the Professional Air Traffic Controllers Organization were imprisoned yhesterday for refusing to obey court orders to end their role in the strike.One, Steven L. Wallaert, president of PATCO Local 291, was taken to Fairfax County jail after telling a federal judge in Alexandria that he intended to stay on strike. Four other union leaders were sent to jail by a federal judge in Kansas City, Kan., later in the day.

The jailings angered many rank-and-file union members, who said the actions had strengthened their resolve to stay off the job.

"When something like this happens, we come together even more," said a Kansas PATCO member who requested anonymity.

Union officials here and elsewhere claimed that only 411 of 13,000 PATCO members who went on strike at 7 a.m. Monday had returned to work yesterday. The union has nearly 15,000 members. According to PATCO calculations yesterday, the strike was still about 81 percent effective, a drop of about four points since the strike began.

But Transportation Secretary Drew Lewis said that 471 striking controllers came in yesterday and 93 others called to say they will be there today. The government contends that from 38 to 40 percent of the workforce was on the job, a figure that apparently included supervisory and other non-union personnel, and that scheduled air traffic was at 75 percent of normal volume.

PATCO President Robert E. Poli said Yesterday that his members intend to stay on strike as long as the government refuses to discuss what he says are the union's "legitimate demands" -- a shorter workweek without reduction in pay, an early retirement plan and higher wages.

Lewis, under orders from President Reagan, has refused to negotiate with the union during the illegal strike. Lewis said yesterday that the administration is more concerned about "how we rebuild the system" once the thousands of expected controller terminations take effect.

The secretary repeatedly has said he will work from a Federal Aviation Administration register of 9,000 applicants for controller jobs, all of whom, according to an FAA spokesman, have passed a basic aptitude exam.

FAA administrator J. Lynn Helms said yesterday that since the strike began his agency has received calls and letters from about 20,000 people seeking controller jobs, which pays an average of $33,000 a year.

Lewis and Helms concede it will not be easy to replace thousands of highly skilled controllers. The training is expensive -- up to $175,000 per trainee -- and controllers must be on the job two to six years before reaching journeyman status.

Lewis has said the nation's air traffic control system might have to operate with reduced staffing for "one or two or three years" because of the firings. In the meantime, he said yesterday, the flying public will have "no cakewalk." But the administration said the incovenience is preferable to yielding to a strike undertaken in violation of federal law.

Poli insisted yesterday that his members "make the system run" and that the government is deluding itself if it thinks it can operate the system without them. "I can only tell you that I know they cannot do it," Poli said.

Meanwhile, the Fedeal Labor Relations Authority said it would hold hearings Monday on a complaint issued by the FLRA general counsel's office accusing PATCO of unfair labor practices.

The complaint was issued at 10 a.m. Monday, three hours after the strike began. The FLRA deals only with federal employes and their unions. In the case of an illegal work stoppage, the authority could decertify a union, revoke its right to act as the exclusive bargaining agent for the workers it represents.

But FLRA officials emphasized yesterday that they can take other actions against PATCO, exclusive of decertification. Suspension of representational rights and more fines were given as examples.

PATCO came close to decertification in 1971, when the FLRA suspended its representational rights for 60 days. The cause was an illegal "job action," a combination slow-down and sickout in 1970.

Public sector unions across the country are concerned that a fullscale decertification of PATCO could set an example for state and local authorities.

Discussions in this regard were under way yesterday at the American Federation of Government Employes, according to AFGE sources who said the union sympathized with the walkout but was concerned about long-term effects of federal sector collective bargaining.

The airline industry says the current conflict is costing the airlines nearly $10 million a day in reduced passenger loads, but Lewis and Helms said yesterday that air traffic was flowing rather well, with about three-quarters of scheduled commercial flights taking off.

Poli said about 50 percent of traffic was moving normally.