With the exponential growth of mobile communications, Small Cell Base Stations (SCBSs) have emerged as an inevitable solution for 5G networks. Nevertheless, due to the significant design challenges associated with providing a reliable energy source for each installation, a wide deployment of SCBSs has not yet happened. In this paper a novel methodology for selecting the optimal power architecture for 5G SCBSs is presented. This approach overcomes the limitations of traditional design strategies by implementing a graph theory-based derivation of the possible configurations. The proposed methodology implements detailed models of the system components, enabling the inclusion of real operating conditions. Multi-objective optimization is selected as the decision-making tool, providing a better understanding of the trade-off between the decision metrics: cost, efficiency, and reliability. Finally, the optimal architecture of a green 5G SCBS in a microgrid-based scenario is obtained.