The ALPINE project benefits from the panchromatic observations of z ~ 5 star-forming galaxies providing fundamental information about their gas/dust content, their morphological and kinematical properties and mechanisms influencing their baryonic cycle highlighted in the studies in recent years. In this work, we make use of chemical evolution models to probe the baryonic evolution of these galaxies. We utilize panchromatic observations to perform spectral energy distribution fitting for these galaxies, employing both Chabrier and top-heavy initial mass functions (IMFs) to derive the physical parameters (i.e stellar mass, star formation rate and dust mass). The chemical evolution models account for dust production, dust growth in the interstellar medium and different destruction mechanisms. Our models successfully reproduce the gas and dust content in most of these primordial galaxies, indicating dust production primarily through Type II supernovae and gas/dust removal via galactic outflows and moderate inflow of primordial gas. Furthermore, a subset of these galaxies displays rapid dust build-up in shorter timescales, which is partially reconcilable with a top-heavy IMF. These findings, coupled with upcoming studies driven by James Webb Space Telescope observations, bridge the gap between observations and models, shedding new light on dust production mechanisms in the early universe.