The Arlington County Board has whittled the list of candidates under consideration for the upcoming vacancy on the county's School Board from nine to five.

The paring came last Saturday after the County Board held a hearing on the vacancy, as required under a new state law, and set a May 5 public forum at which County Board members will interview the remaining applicants.

The Democrat-controlled County Board will select a successor sometime in May for Margaret A. Bocek, the only Republican on the five-member School Board. The appointed successor to Bocek, whose four-year term expires June 30, will in all likelihood be a Democrat.

Unlike in past years, the County Board's only Republican member, Michael E. Brunner, will not participate in the appointment process because of recent court rulings.

Brunner cited a 1984 Virginia Supreme Court ruling that bars participation in school-related votes by elected officials who work for or have relatives working in the affected school system.

Brunner's wife, Elizabeth, is a part-time school psychologist who has been on the school staff for 16 years, predating both her husband's election to the County Board in 1983 and, previously, his appointment to the School Board in late 1981.

Lower courts have since issued rulings similar to the 1984 decision, which grew out of a Richmond case in which a city council member was barred from voting on school issues because he was also a principal.

Brunner said he learned of the rulings only a few weeks ago and would abstain from voting on Bocek's replacement to avoid any potential conflict of interest. He also abstained last week when the County Board adopted the school-related portion of the fiscal 1987 budget.

Arlington delegates to the General Assembly were unable to win an exemption for Brunner in the last session during debate over other parts of the state's conflict-of-interest laws.

Brunner said he believed the ruling was "far too constraining and was not intended for people like me," but would not take part in the appointment process "to be sure everything is on the up and up."

That will leave the board's four Democrats to select the next School Board member. The five candidates are: Edward R. Hilz, a Federal Labor Relations Authority senior labor relations specialist who has chaired the Arlington Civic Federation schools committee since 1983 and has been active in the Fairlington Citizens Association and the County Council of PTAs. Steven D. Ivins, tax editor for Kiplinger Washington Editors Inc., who has been active in several capacities with the County Council of PTAs and who has served on several School Board and County Board advisory committees as well as on the board of the Rivercrest Civic Association. Harry G. Lilly, the owner of and an executive with Vicore Inc., a human resources development consulting firm, who has been active in the County Council of PTAs, various School Board advisory groups and several civic groups, including the civic federation and the Committee of 100. Conchita Mitchell, president of the County Council of PTAs since 1984 and vice president the year before, who has served on various School Board advisory committees and regularly attends board meetings. Edward G. Modell, an attorney with Blum Nash & Railsback, who is chairman of the school budget subcommittee of the County Board's fiscal affairs advisory committee and the school budget committee of the County Council of PTAs, and who has also served on School Board advisory committees.