The article aims (1) to evaluate material flows in the manufacturing process reflecting the level of circular manufacturing of European Union countries and (2) to estimate the relationship between the level of circular manufacturing and the volume of e-waste put on the market, illustrating the implementation effect of Industry 5.0 technologies. A systematic country classification was created according to development conditions for environmentally sustainable enterprises and trends in e-waste volumes. Multidimensional data analysis and the linear ordering method were used to achieve the research objectives. The dynamics of changes in the identified variables were analysed using dynamics indexes and the average annual rate of change. Relationships were estimated using Pearson’s linear correlation coefficient. The main research result is the estimated synthetic development measure illustrating the level of circular manufacturing in the context of material flows. Significant differences were observed between the synthetic development measure values representing the level of circular manufacturing in European Union countries. This means countries’ circular manufacturing levels are significantly higher than others. Moreover, the values of correlation coefficients were estimated between the level of circular manufacturing and the volume of e-waste put on the market and between the average annual rate of change of the synthetic development measure and the average annual rate of change of the e-waste volume. The coefficient values do not confirm a statistically significant relationship between the indicated variables. Most countries have average conditions for developing environmentally sustainable businesses, but at the same time, they show negative trends in the volume of e-waste generated.