I present a minimal $SU(5)$ model with an additional $U(1)$ Peccei-Quinn symmetry that predicts the existence of an ultralight axion dark matter with a mass between 0.1 neV and 4.7 neV. I furthermore argue that the entire parameter space of the proposed model will be probed through a synergy between several low-energy experiments that look for proton decay (Hyper-Kamiokande), axion dark matter through axion-photon coupling (ABRACADABRA and DMRadio-GUT), and nucleon electric dipole moments (CASPEr Electric).