  Measurements of the size of dust continuum emission are an important tool for
constraining the spatial extent of star formation and hence the build-up of
stellar mass. Compact dust emission has generally been observed at Cosmic Noon
(z~2-3). However, at earlier epochs, toward the end of the Reionization
(z~4-6), only the sizes of a handful of IR-bright galaxies have been measured.
In this work, we derive the dust emission sizes of main-sequence galaxies at
z~5 from the ALPINE survey. We measure 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 compare it with rest-frame UV and [CII]158$\mu$m measurements. We study the
r_e,FIR-L_IR scaling relation by considering our dust size measurements and all
the data in literature at z~4-6. Finally, we compare our size measurements with
predictions from simulations. The dust emission in the selected ALPINE galaxies
is rather extended (r_e,FIR~1.5-3 kpc), similar to [CII]158 um but a factor of
~2 larger than the rest-frame UV emission. Putting together all the
measurements at z~5, spanning 2 decades in luminosity from L_IR ~ 10^11 L_sun
to L_IR ~ 10^13 L_sun, the data highlight a steeply increasing trend of the
r_e,FIR-L_IR relation at L_IR< 10^12 L_sun, 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 sub-set of galaxies (~25% at 10^10 M_sun < M_star < 10^11 M_sun) with
sizes as large as those measured.
