Predicting future climatic conditions at high spatial resolution is essential for many applications in science. Here we present data for monthly time series of precipitation and minimum and maximum temperature for four downscaled global circulation models. We used model output statistics in combination with mechanistic downscaling (the CHELSA algorithm) to calculate mean monthly maximum and minimum temperatures, as well as monthly precipitation sums at ~5km spatial resolution globally for the years 1850-2100. We validated the performance of the downscaling algorithm by comparing model output with observed climates for the years 1950-2069. CHELSA_cmip5_ts is licensed under a Creative Commons Attribution 2.0 Generic (CC BY 2.0) license.