Impact glasses found in lunar soils provide a possible window into the impact history of the inner solar system. However, their use for precise reconstruction of this history is limited by an incomplete understanding of the physical mechanisms responsible for their origin and distribution and possible relationships to local and regional geology. Here, we report U-Pb isotopic dates and chemical compositions of impact glasses from the Chang'e-5 soil and quantitative models of impact melt formation and ejection that account for the compositions of these glasses. The predominantly local provenance indicated by their compositions, which constrains transport distances to <~150 kilometers, and the age-frequency distribution are consistent with formation mainly in impact craters 1 to 5 kilometers in diameter. Based on geological mapping and impact cratering theory, we tentatively identify specific craters on the basaltic unit sampled by Chang'e-5 that may have produced these glasses and compare their ages with the impact record of the asteroid belt.