Aberrant epigenetic regulation is closely associated with drug tolerance, an early step in the acquisition of drug resistance. We previously reported that a pioneer transcriptional factor (also called an epigenetic initiator) rapidly induced by osimertinib, a third-generation epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor, plays a pivotal role in promoting the formation of osimertinib-tolerant cells. In this study, to identify novel epigenetic factors associated with osimertinib-tolerance, we performed a comprehensive screening of epigenetic factors whose expression is rapidly induced by osimertinib. Our results revealed that HDAC5, a class IIa histone deacetylase (HDAC), is a prominently induced epigenetic regulator in several EGFR-mutant non-small cell lung cancer (NSCLC) cell lines during the early response to osimertinib. Knockdown of HDAC5 significantly reduced the emergence of osimertinib-resistant cells. Furthermore, treatment with LMK235, a selective HDAC5 inhibitor, significantly increased global histone acetylation and enhanced osimertinib-induced apoptosis. These findings highlight the potential of HDAC5 as a novel therapeutic target to overcome osimertinib-resistance and suggest LMK235 as a promising compound to provide therapeutic benefit to EGFR-mutant NSCLC patients receiving osimertinib treatment.