Measurements of the size of dust continuum emission are an important tool for constraining the spatial extent of star formation, and hence the buildup of stellar mass.
Compact dust emission has generally been observed at cosmic noon ($z $). However, at earlier epochs, toward the end of the reionization ($z $), only the sizes of a handful of infrared (IR) bright galaxies have been measured. In this work, we derive the dust emission sizes of main-sequence (MS) galaxies at $z from the ALPINE survey. We measured the dust effective radius, $r_ e,FIR $, in the uv-plane in Band 7 of ALMA for seven ALPINE galaxies with resolved emission and we compared it with rest-frame ultraviolet (UV) and CII 158mu m measurements. We studied the $r_ e,FIR -$L$_ IR $ scaling relation by considering our dust size measurements and all the data in the literature at $z $. Finally, we compared our size measurements with predictions from simulations. The dust emission in the selected ALPINE galaxies is rather extended ($r_ e,FIR $ kpc), similar to CII 158mu m but a factor of sim 2 larger than the rest-frame UV emission. Putting together all the measurements at $z spanning two decades in luminosity from IR $ L$_ to IR $ L$_ the data highlight a steeply increasing trend of the e,FIR -$L$_ IR $ relation at L$_ IR $ L$_ followed by a downturn and a decreasing trend at brighter luminosities. Finally, simulations that extend up to the stellar masses of the ALPINE galaxies considered in the present work predict a subset of galaxies ( $ <!PCT!> at 1010 sun < $M$_ $ M$_ sun $) with sizes as large as those measured.