The efficient and timely degradation of proteins is crucial for many cellular processes and to maintain general proteostasis. The proteasome, a complex multisubunit protease, plays a critical role in protein degradation. Therefore, it is important to understand the assembly, regulation, and localization of proteasome complexes in the cell under different conditions. Fluorescent tags are often utilized to study proteasomes. A GFP-tag on the β5 subunit, one of the core particle (CP) subunits with catalytic activity, has been shown to be incorporated into proteasomes and commonly used by the field. We report here that a tag on this subunit results in aberrant phenotypes that are not observed when several other CP subunits are tagged. These phenotypes appear in combination with other proteasome mutations and include poor growth, and, more significantly, altered 26S proteasome localization. In strains defective for autophagy, β5-GFP tagged proteasomes, unlike other CP tags, localize to granules upon nitrogen starvation. These granules are reflective of previously described proteasome storage granules but display unique properties. This suggests proteasomes with a β5-GFP tag are specifically recognized and sequestered depending on physiological conditions. In all, our data indicate the intricacy of tagging proteasomes, and possibly, large complexes in general.