Complex sentence: The peak of his career was from 1939 to 1947, after which drug use led to his decline, and with the rising popularity of rock and roll among teenagers in the 1950s, older musicians were not in high demand.
Split into simpler sentences: The peak of his career was from 1939 to 1947. His own drug use led to his decline, and with the rising popularity of rock and roll among teenagers in the 1950s, older musicians were not in high demand.