They had 5 children: Erich Pringsheim, Peter Pringsheim, Heinz Pringsheim, Klaus Pringsheim Sr. and Katia Pringsheim who married Thomas Mann.
This passage describes a family with five members: Erich Pringsheim, Peter Pringsheim, Heinz Pringsheim, Klaus Pringsheim Sr., and Katia Pringsheim.  Katia Pringsheim's marriage to Thomas Mann is highlighted.