Five District hospitals sought permission yesterday from the city's health planning commission to perform heart transplants.

Four of the hospitals -- Washington Hospital Center, George Washington University Medical Center, Howard University Hospital and Children's Hospital -- have applied together. Georgetown University Hospital also has submitted a request.

In a public hearing on the requests, Sharyl Kiger, an assistant administrator at Georgetown, said the hospital dropped out of the group application after a majority of the hospitals decided that the transplants would be performed at the Washington Hospital Center. Georgetown had wanted "a consortium without walls," Kiger said.

Georgetown's experience with tissue typing and other transplant-related practices were instrumental in Fairfax Hospital winning approval from Virginia health authorities to perform heart transplants. In its application, Fairfax said Georgetown will provide tissue typing and other medical help for its heart program.

Spokesmen for the group application emphasized the volume of related surgeries its member hospitals perform: 154 kidney transplants and 1,498 open heart operations in 1985.

Because of the cost of duplicating services, the U.S. Department of Health and Human Services is working on rules to limit the number of heart transplant centers.

The District's health agency set up a technical advisory panel to evaluate the requests. A decision is not expected for several months.