Differing reports regarding the structural features of the mineral stützite, Ag5-xTe3 (-0.25 ≤ x ≤ 1.44), and the quest for tellurides with low-dimensional fragments stimulated our impetus to review this system by employing experimental as well as quantum-chemical methods. Determination of the crystal structures for three samples with compositions Ag4.72(3)Te3 (I), Ag4.66(1)Te3 (II), and Ag4.96(2)Te3 (III) revealed considerable positional disorders for the Ag and Te sites and previously unknown structure models for I and II, which differ from that of III through the stacking sequences of honeycomb-fashioned Te layers. The crystal structures comprise [Te@Ag9]@Te14 units in the forms of bicapped hexagonal Te antiprisms that enclose Te-centered tricapped trigonal Ag prisms, while each Te atom is encapsulated by Ag atoms assembling diverse types of coordination polyhedra. The vibrational and electronic properties were determined for three models approximating the actual crystal structure of stützite by means of techniques based on first principles. From analyses of the electronic structures and projected crystal orbital Hamilton populations (pCOHP), it is clear that the amounts and distributions of the Ag atoms within the Te network should be influenced by the subtle interplay between the attempts to achieve an electronically favorable situation with a gap at EF and minimize the occupations of antibonding states.