Free energy landscapes decisively determine the progress of enzymatically catalyzed reactions1. Timeresolved macromolecular crystallography unifies transient-state kinetics with structure determination2-4 because both can be determined from the same set of X-ray data. We demonstrate here how barriers of activation can be determined solely from five-dimensional crystallography5. Directly linking molecular structures with barriers of activation between them allows for gaining insight into the structural nature of the barrier. We analyze comprehensive time series of crystallographic data at 14 different temperature settings and determine entropy and enthalpy contributions to the barriers of activation. 100 years after the discovery of X-ray scattering, we advance X-ray structure determination to a new frontier,the determination of energy landscapes.