Catalyzes the decarboxylation of mevalonate 5-phosphate (MVAP) to isopentenyl phosphate (IP). Functions in an alternate mevalonate (MVA) pathway leading to isopentenyl diphosphate (IPP), a key precursor for the biosynthesis of isoprenoid compounds such as archaeal membrane lipids. (R)-5-phosphomevalonate + ATP = ADP + CO2 + isopentenyl phosphate + phosphate Is strongly inhibited by 6-fluoromevalonate monophosphate but shows negligible inhibition by 6-fluoromevalonate diphosphate (a potent inhibitor of the classical mevalonate pathway). kcat is 3.5 sec(-1). Optimum pH is about 7.5. Belongs to the phosphomevalonate decarboxylase family.