© 2015 American Physical Society. We combine magnetization, pressure-dependent electrical resistivity, and heat capacity measurements to investigate the physical properties of the novel compound UAuBi2. Our single crystals, grown by the self-flux method, share the same tetragonal HfCuSi2-type structure as their Ce-based counterparts. UAuBi2 shows ferromagnetic ordering at Tc=22.5 K, in contrast with the antiferromagnetic transition found in CeAuBi2 (TN=12K) but closely related to UAuSb2 (Tc=31K). Despite the differences, all compounds display an easy axis of magnetization along the c axis and a large magnetocrystalline anisotropy. The heat capacity and pressure-dependent resistivity suggest that UAuBi2 exhibits moderately heavy-fermion behavior (γ∼100mJ/mol·K2) with strongly localized 5f electrons. An intricate competition between crystalline electric field (CEF) effects and two anisotropic exchange interactions (JRKKY) persists in the 5f system, which leads to the striking difference between ground states. A systematic analysis of our macroscopic data using a mean-field model including anisotropic JRKKY interactions and the tetragonal CEF Hamiltonian allows us to extract the CEF scheme and the values of JRKKY. Our results suggest a general trend in this family of compounds and shed light on the similarities and differences between 4f and 5f members.