The protein phosphatase 5 (PP5) is normally recruited to its substrates by the molecular chaperones, heat shock protein 70 (Hsp70) and heat shock protein 90 (Hsp90). This interaction requires the tetratricopeptide repeat (TPR) domain of PP5, which binds to an EEVD motif at the extreme C-termini of cytosolic Hsp70 and Hsp90 isoforms. In addition to bringing PP5 into proximity with chaperone-bound substrates, this interaction also relieves auto-inhibition in PP5's catalytic domain, promoting its phosphatase activity. To better understand the molecular determinants of this process, we screened a large, pentapeptide library for binding to PP5. This screen identified the amino acid preferences at each position, which we validated by showing that the optimal sequences bind 4- to 7-fold tighter than the natural EEVD motifs and stimulate PP5's enzymatic activity. The enhanced affinity for PP5's TPR domain was confirmed using a protein-adaptive differential scanning fluorimetry (paDSF) assay. Using this increased knowledge of structure-activity relationships, we re-examined affinity proteomics results to look for potential EEVD-like motifs in the C-termini of known PP5-binding partners. This search identified elongator acetyltransferase complex subunit 1 (ELP1/IKBKAP) as a putative partner and, indeed, we found that its C-terminal sequence, LSLLD, binds directly to PP5's TPR domain in vitro. Consistent with this idea, mutation of ELP1's terminal aspartate was sufficient to interrupt the interaction with PP5 in vitro and in cells. Together, these findings reveal the sequence preferences of PP5's TPR domain and expand the scope of PP5's functions to include chaperone-independent complexes.