Each solar maximum interval has a different duration and peak activity level, which is reflected in the behavior of key physical variables that characterize solar and solar wind driving and magnetospheric response. The variation in the statistical distributions of the F10.7 index of solar coronal radio emissions, the dynamic pressure P Dyn and effective convection electric field E y in the solar wind observed in situ upstream of Earth, the ring current index D ST , and the high-latitude auroral activity index AE are tracked across the last five solar maxima. For each physical variable we find that the distribution tail (the exceedences above a threshold) can be rescaled onto a single master distribution using the mean and variance specific to each solar maximum interval. We provide generalized Pareto distribution fits to the different master distributions for each of the variables. If the mean and variance of the large-to-extreme observations can be predicted for a given solar maximum, then their full distribution is known.Plain Language Summary Earth's near-space plasma environment is highly dynamic, with its own space weather. Space weather impacts include electrical power loss, aviation disruption, interrupted communications, and disturbance to satellite systems. The drivers of space weather, the sun and solar wind, and the response seen at Earth have now been almost continually monitored by ground-and space-based observations over the last five solar cycles (more than 50 years). Each of the last five solar maxima has a different duration and peak activity level and as a consequence the climate of Earth's space weather is also different at each solar maximum. We find that some aspects of the space weather climate are in fact reproducible; they can be inferred from that of previous solar maxima. This may help understand the behavior of future solar maxima.