Earth’s core may contain C, and it has been suggested that C in the core could stabilize the formation of a solid inner core composed of Fe₃C. We experimentally examined the Fe–C system at a pressure of 5GPa and determined the Fe–C phase diagram at this pressure. In addition, we measured solid metal/liquid metal partition coefficients for 17 trace elements and examined the partitioning behavior between Fe₃C and liquid metal for 14 trace elements. Solid metal/liquid metal partition coefficients are similar to those found in one atmosphere studies, indicating that the effect of pressure to 5GPa is negligible. All measured Fe₃C/liquid metal partition coefficients investigated are less than one, such that all trace elements prefer the C-rich liquid to Fe₃C. Fe₃C/liquid metal partition coefficients tend to decrease with decreasing atomic radii within a given period. Of particular interest, our 5GPa Fe–C phase diagram does not show any evidence that the Fe-Fe₃C eutectic composition shifts to lower C contents with increasing pressure, which is central to the previous reasoning that the inner core may be composed of Fe₃C.