Dirac semimetals feature Dirac cones with topologically nontrivial states in the bulk that are protected by crystalline symmetries. They attract considerable attention due to rich quantum states and properties of interest, such as high Fermi velocities, mobility, and small effective masses. Here, we show that a ternary intermetallic BaAuSb crystal hosts both trivial and nontrivial topological Dirac states in the bulk. The nontrivial Fermi-surface pocket at the Brillouin zone center is characterized with only a few hundredths of a bare electron mass and with very high mobility. All parts of the Fermi surface detected by quantum oscillations, topologically trivial or nontrivial, have carriers with unusually high Fermi velocities and small masses. These conducting states may be coupled with magnetic moments in materials where Ba is replaced by magnetic rare-earth atoms.