The Board of City Directors on Tuesday approved a controversial plan by Caltech to build a five-story, 475-space parking garage on the western edge of the campus in Pasadena. Nearby residents complained that the structure would be an eyesore in their neighborhood and urged the board to prohibit it. Caltech officials said the structure is needed to provide student and faculty parking. The structure is to be built on Wilson Avenue, between San Pasqual Street and Del Mar Boulevard. Ten houses and a triplex now being used for student housing will be demolished to make way for the garage. City officials said Caltech's plans to build a 156-room dormitory will compensate for the lost housing.