Performs the first committed step in the biosynthesis of isoprene-containing compounds such as sterols and terpenoids (By similarity). Component of the triterpene saponins (e.g. ginsenosides or panaxosides) and phytosterols biosynthetic pathways (PubMed:29378087). Catalyzes the conversion of mevalonate diphosphate to isopentenyl diphosphate (IPP) (PubMed:29509695). (R)-5-diphosphomevalonate + ATP = ADP + CO2 + isopentenyl diphosphate + phosphate Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via mevalonate pathway; isopentenyl diphosphate from (R)-mevalonate: step 3/3. Homodimer. Belongs to the diphosphomevalonate decarboxylase family.