A 32-year-old secretary on a lunchtime shopping trip became the Washington subway's 5 millionth passenger yesterday, more than a year sooner than Metro officials expected that milestone to be reached.

Despite the unexpectedly high level of riding, it is costing more than $7 to run the rail line for every $1 that is being collected in fares. The costs were expected, a Metro financial official said, because the first 5-mile line is bearing heavy expenses for training and other items that should decline as more trackage is opened.

The 5 millionth passenger was Jackie Eisenhardt of Oakton, Va., a secretary for the Air Line Pilots Association. She was chosen by countdown at the Metro Center subway station shortly after 2 p.m. on the basis of ridership statistics kept since regular service began last March 29.

Only when the camera lights falshed in her face and Metro board chairman Francis W. White stepped into her path for a greeting did she learn of her status. She was given a gold-plated token encased in a transparent lucite cube and a free ride back to her office.

Metro planners initially forecast that only about 8,000 passengers a day would ride the first line, now 5 miles long. The actual total - swelled by midday riders like Mrs. Eisenhardt - is averaging above 27,000.

At the lower predicted rate, White told Mrs. Eisenhardt, she might have been the 2 millionth passenger, not the 5 millionth. However, future projections are distorted by plans to open the second subway route July 1.

"It was my first time (on the subway)," Mrs. Eisenhardt told White, explaining that she had gone from her office with a fellow worker, Michele Wright, to shop at Woodward & Lothrop. The department store has a direct entry from the Metro Center station mezzanine.

Despite, the larger-than-predicted number of passengers, the first line is running up a heavy loss.

Metro's most recent official report, covering the five months from last July through November, showed fare collections and other revenues, such as parking fees at the Rhode Island Avenue station and advertising income, totaling $987,017. Expenses were nearly $7.5 million, leaving a cash shortfall of about 6.5 million.

Fritz Becker, Metro's acting budget director, said this is not - strictly speaking - a deficit, since the costs of training, including the expense of running empty trains at odd hours, is included. He said various costs for such things as fare collection, security and train control will drop proportionately as the system is lengthened.

Under an agreement with the U.S. Department of Transportation, area governments will have to contribute only $1.8 million in current subsidy payments in this fiscal year, with the balance, but $20 million, to come from capital funds previously earmarked for subway construction.