Five daily passenger trains serving Washington would be eliminated under the new Amtrak system plan recommended yesterday by the Department of Transportation.

Amtrak, however, would take over operation of the Southern Crescent, from Washington to New Orleans via Atlanta. The Southern Railway, which runs the Crescent now, has asked the Interstate Commission to drop the train, which it said loses more than $500,000 a month.

Scheduled to be eliminated by July 1, 1980, if DOT adopts the recommendations are:

The Shenandoah, from Washington to Cincinnati via Harpers Ferry and Cumberland.

The Blue Ridge, from Washington to Martinsburg, W. Va. via Harpers Ferry.

The Hilltopper from Washington to Catlettsburg, Ky., via Richmond and Roanoke.

The Colonial, from Boston to Newport News, via Washington.

The Washington section of the National Limited, which not has separate sections from Washington and New York to Los Angeles.

Washington passengers could still catch the National Limited, but instead of boarding their car at Union Station, they would have to ride another train to North Philadelphia station, then change of the train from New York.

Except for the Blue Ridge, which carries mostly commuters, none of the trains carries the 100 passengers per mile minimum recommended by DOT.

None of the trains can be dropped until public hearings have been held and until Congress has approved DOT's new Amtrak system plan.

Heavy political opposition is expected on at least one of the endangered Washington trains, the Shenandoah, which serve the congressional district of Rep. Harley Staggers (DMW. Va.), chairman of the House Commerce Committee.

Averaging only 33 passengers per mile - lowest in the Amtrak system - the Shenandoah loses $1.4 million a year, DOT estimates.

Running over the same tracks as far as Martinsburg, the Blue Ridge carries 500 passengers a day, an Amtrak spokesman said. But most of the passengers are commuters and the DOT report says commuter rail service should not be Amtrak's responsibility.