This paper presents a five-level bi-directional flying capacitor DC-DC converter topology for energy management application in a DC microgrid. Unlike traditional two-level DC-DC converter, the presence of multiple flying capacitors in this topology brings the possibility of having a higher voltage-gain conversion ratio at enhanced efficiency. The existence of five voltage levels give the converter an advantage of having reduced voltage stress on its power switches and a low-sized inductor filter at its input. Additionally, the capability of having bi-directional power flow enables the converter to integrate energy storage devices such as the battery to a high voltage DC microgrid effectively. A finite control set - model predictive control (FCS-MPC) algorithm is formulated using the developed mathematical model in order to yield the multi-objective of bi-directional power flow and three flying capacitor voltage balancing. Furthermore, a DC microgrid comprising photo-voltaic (PV) system, load, and battery are considered to assess the effectiveness of the designed FCS-MPC algorithm under varying load and PV power injections.