Catalyzes the phosphorylation of mevalonate to mevalonate 5-phosphate, a key step in isoprenoid biosynthesis. (R)-mevalonate + ATP = (R)-5-phosphomevalonate + ADP + H(+) Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via mevalonate pathway; isopentenyl diphosphate from (R)-mevalonate: step 1/3. Belongs to the GHMP kinase family. Mevalonate kinase subfamily.