A process for the separation of C5+ cuts by distillation into a low-boiler, a medium-boiler and a high-boiler fraction in at least one thermally coupled column, where the low-boiler fraction and the high-boiler fraction are withdrawn from different columns, and the operating pressure of the column from which the high-boiler fraction is withdrawn is set from 0.1 to 2 bar lower than the operating pressure of the column from which the low-boiler fraction is withdrawn, with the at least one column arranged to have different regions wherein there is formation of an upper, common column region, a lower, common column region, a feed part with rectifying section and stripping section, and a withdrawal part with rectifying section and stripping section, with feed of the C5+ cut into the central region of the feed part, discharge of the high-boiler fraction from the bottom of the column, discharge of the low-boiler fraction via the top of the column, and discharge of the medium-boiler fraction from the central region of the withdrawal part, wherein the different regions may be in different columns, and wherein the dividing ratio of the liquid reflux at the upper end of the at least one thermally coupled column is set in such a way that the proportion of high-boiling key components in the liquid reflux over the stripping section of the withdrawal part at the upper end of the at least one thermally coupled column is from 10 to 80% of a limit value allowed in the medium boiler fraction, and wherein a heating power in an evaporator at the bottom of the at least one thermally coupled column is set in such a way that the concentration of the low-boiling key components in the liquid at the lower end of the at least one thermally coupled column is from 10 to 80% of the limit value allowed in the medium-boiler fraction.