5G mobile devices and base stations will be operating antenna arrays and beam-steering techniques in the millimeter-wave region. The question of the far-field measurement distance is particularly critical for such technologies as a larger over-the-air test range means dynamic range issues and significantly larger cost. The traditionally used formula for the far-field distance aims at limiting the impinging field phase curvature. Using this criterion leads to testing distances of more than 6 meters to assess the far-field radiation pattern of a 5G smartphone equipped with 39 GHz transceiver. This paper investigates the physical relevance of such a large distance. It uses spherical wave expansion theory to establish two new far-field distance definitions, including considerations on the antenna directivity. An initial set of measurement data is provided to support the findings that much shorter distances than commonly known can be used for accurate far-field evaluation in the main radiation beam.