This work investigates how to promote energy and carbon-efficient video streaming in 5G networks by encouraging users to accept lower streaming bitrates while maintaining a positive perceived quality of experience (QoE). It introduces a user-centric probabilistic acceptance model that considers environmental awareness, individual responsiveness to incentives, altruistic behaviour, and social well-being motivations. The proposed framework uses personalized, adaptive incentives, provider-led education strategies, and data-driven learning from user interactions to gradually improve acceptance of sustainable streaming practices. The results demonstrate that incentive and behavioural adaptation can help reduce network energy consumption while balancing user satisfaction, provider costs, and sustainability objectives. This research is conducted within the framework of the broader European Union project EXIGENCE, which aims to advance sustainable and energy-efficient digital infrastructures. The work was presented at the IEEE International Conference on Communications (ICC) 2026.