Catalyzes the phosphorylation of mevalonate to mevalonate 5-phosphate, a key step in isoprenoid and cholesterol biosynthesis. (R)-mevalonate + ATP = (R)-5-phosphomevalonate + ADP + H(+) Its activity is inhibited in vitro by geranyl pyrophosphate (GPP) and farnesyl pyrophosphate (FPP) that bind competitively at the ATP-binding site on the enzyme. 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.