Profile, Always High, Keeps Current Too.

IT was sometime in the mid-1980s, Carol Peligian recalls, that she told her broker not to telephone her until she'd found her an apartment among the run-down, sparsely populated commercial blocks of Fifth Avenue between 14th and 23rd Streets. The broker's response was succinct: ''You're out of your mind.'' Ms. Peligian's husband, Robert Boghosian, was scarcely more enthusiastic. But Ms. Peligian, an artist, recognized New York as a great shape-shifting organism; she felt that the decidedly unglamorous area below Madison Square Park might have a future to match its richly textured past. At the time, that stretch of Fifth Avenue was ''like a canyon: it was abandoned, it was vast and boarded up,'' she said. ''But it had a faded old beauty just waiting to be cared for a little bit.'' [ABSTRACT FROM AUTHOR]