The Dells were consultants in that Robert Townend (writer and director) went on tour with them. But given The Dells hold the record as the group with the same line up for the longest period I would not say it was based on them. Nobody left the Dells or died of drugs. If you watch the film the group that springs to mind is the Temptations.
All Movie guide says this
Plot Synopsisby Hal EricksonLoosely based on the life and times of several R&B artists (The Dells, The Temptations, Frankie Lymon, Sam Cooke and others) The Five Heartbeats traces the rise and fall of a popular African-American 1950s singing aggregation. The story is told from the point of view of one of the "Heartbeats," played by Robert Townsend (who also co-produced, directed and co-wrote the script with Keenan Ivory Waynans). The film is an amalgam of anecdotes drawn from real-life experiences: the long struggle upward, the first rush of success, the dishonest record-company executives, the hard-nosed but nurturing managers, the sex, the drugs, the isolation and the precipitous downward slide. The film begins and ends in the 1990s, as the middle-aged "Duck" (Townsend) ruminates on the past and makes the best of the present.