Histone demethylase that specifically demethylates 'Lys-4' of histone H3, thereby playing a central role in histone code. Does not demethylate histone H3 'Lys-9', H3 'Lys-27', H3 'Lys-36', H3 'Lys-79' or H4 'Lys-20'. Demethylates trimethylated and dimethylated but not monomethylated H3 'Lys-4'. Regulates specific gene transcription through DNA-binding on 5'-CCGCCC-3' motif (PubMed:18270511). May stimulate transcription mediated by nuclear receptors. Involved in transcriptional regulation of Hox proteins during cell differentiation (PubMed:19430464). May participate in transcriptional repression of cytokines such as CXCL12. Plays a role in the regulation of the circadian rhythm and in maintaining the normal periodicity of the circadian clock. In a histone demethylase-independent manner, acts as a coactivator of the CLOCK-BMAL1-mediated transcriptional activation of PER1/2 and other clock-controlled genes and increases histone acetylation at PER1/2 promoters by inhibiting the activity of HDAC1 (By similarity). Seems to act as a transcriptional corepressor for some genes such as MT1F and to favor the proliferation of cancer cells (PubMed:27427228). {ECO:0000250|UniProtKB:Q3UXZ9, ECO:0000269|PubMed:11358960, ECO:0000269|PubMed:15949438, ECO:0000269|PubMed:17320160, ECO:0000269|PubMed:17320161, ECO:0000269|PubMed:17320163, ECO:0000269|PubMed:18270511, ECO:0000269|PubMed:19430464, ECO:0000269|PubMed:27427228}. This is the function of Ensembl gene identifier ENSG00000073614 (KDM5A, lysine demethylase 5A).