The increasing demand for quality from multimedia service users is very often addressed by adding more resources (bandwidth and processing power). However, not always does this approach bring an improvement in the perceived quality, whereas it frequently implies an increase in energy consumption (and subsequent higher greenhouse gas emissions). Accordingly, in this paper, we propose a solution to dynamically allocate resources in a 5G heterogeneous network scenario, which aims to identify a trade-off between the overall QoE perceived by the users served by the network when consuming video content and the overall network energy consumption. We considered three types of devices (TV, laptop, and smartphone) for which appropriate QoE and energy consumption models are defined. Extensive simulations have been performed by assigning different levels of importance to QoE and energy. The achieved results show that the network energy consumption can be more than halved by keeping satisfactory QoE. This is particularly true for smartphone users, whereas TV and laptop users have the freedom to choose based on their sensitivity towards sustainability.