Although Geostationary-Equatorial-Orbit (GEO) satellites have achieved significant success in conducting space missions, they cannot meet the 5G latency requirements due to the far distance from the earth surface. Therefore, Low-Earth-Orbit (LEO) satellites arise as a potential solution for the latency problem. Nevertheless, integrating the 5G terrestrial networks with LEO satellites puts an increased burden on the satellites' limited budget, which stems from their miniature sizes, restricted weights, and the small available surface for solar harvesting in the presence of additional required equipment. This paper aims to design the Electrical Power System (EPS) for 5G LEO satellites and investigate altitudes that meet the latency and capacity requirements of 5G applications. In this regard, accurate solar irradiance determination for the nadir-orientation scenario, Multi-Junction (MJ) solar cells modeling, backup batteries type and number, and designing highly-efficient converters are addressed. Accordingly, the power budgeting of the 5G LEO satellite can be achieved based on defining the maximum generated power and determining the satellite's subsystem power requirements for 5G missions. In the sequel, the measured and simulated values of the electrical V-I characteristics of an MJ solar panel are compared to validate the model by using a Clyde Space solar panel that reaches a maximum power generation of approximately 1 W at ( I MPP =0.426 A, V MPP =2.35 V). Moreover, a synchronous boost converter circuit is designed based on commercial off-the-shelf elements.