Industry 5.0 places emphasis on human-centered innovation, aligning digital transformation with sustainability, resilience, and societal well-being. Smart cities serve as practical environments where advanced technologies must balance operational efficiency with environmental responsibility. Since October 2023, deep neural networks have been widely used in urban decision-making, including traffic optimization and environmental monitoring. However, the high energy demand required to train large-scale models has raised concerns regarding both environmental impact and economic cost, leading to growing interest in sustainable AI practices. This study explores Carbon-Aware Neural Network Optimization within the Green AI framework as a practical approach to reduce computational carbon emissions while maintaining predictive performance. Three complementary strategies are integrated into a unified training pipeline and monitored using the CodeCarbon framework: partial layer freezing, quantization-aware training, and adaptive early stopping. Experiments are conducted on CIFAR-10 using MobileNetV2 and on a subset of ImageNet with ResNet-50. Results show a reduction in CO₂ emissions of 52% and 49%, respectively, with only minor changes in model accuracy. The findings indicate that combining these techniques provides an effective balance between efficiency and predictive reliability, supporting the development of sustainable AI solutions for Industry 5.0 and smart city applications.