Catalyzes the transfer of the enolpyruvyl moiety of phosphoenolpyruvate (PEP) to the 5-hydroxyl of shikimate-3-phosphate (S3P) to produce enolpyruvyl shikimate-3-phosphate and inorganic phosphate (By similarity). Involved in the accumulation of volatile benzoides in flowers, scent attracting pollinators (e.g. the night-active hawkmoth pollinator Manduca sexta) (PubMed:15805488). 3-phosphoshikimate + phosphoenolpyruvate = 5-O-(1-carboxyvinyl)-3-phosphoshikimate + phosphate Repressed by glyphosate in a competitive inhibition manner. kcat is 36 sec(-1). Metabolic intermediate biosynthesis; chorismate biosynthesis; chorismate from D-erythrose 4-phosphate and phosphoenolpyruvate: step 6/7. Mostly expressed in flower petals, and, to a lower extent, in roots, stems and anthers, but barely in leaves. Circadian-regulation with peak levels occurring at the end of the light period in flowers; this expression is monitored by ODO1-mediated induction and by LHY binding and repression to cis-regulatory evening elements in its promoter (PubMed:15805488, PubMed:26124104). Triggered by EOBI in flowers (PubMed:23275577). This enzyme is the target of the potent, broad-spectrum herbicide, glyphosate [n-(phosphonomethyl)glycine]. Overproduction of EPSP leads to glyphosate tolerance. Belongs to the EPSP synthase family.