Catalyzes the methylation of C-5 in cobalt-precorrin-7 to form cobalt-precorrin-8. Co-precorrin-7 + S-adenosyl-L-methionine = Co-precorrin-8X + H(+) + S-adenosyl-L-homocysteine Cofactor biosynthesis; adenosylcobalamin biosynthesis; cob(II)yrinate a,c-diamide from sirohydrochlorin (anaerobic route): step 8/10. Belongs to the precorrin methyltransferase family.