How long can a person with rheumatic heart disease live with proper care?

To a ripe old age: Rheumatic heart disease is uncommon today but some that occur sporadically face a common set of problems. After recovery, the disease may have caused valve damage & repair may be needed but is possible. It probably cuts a decade off ones life expectancy, but many of our other bad habits do also.

Normal life : Assuming there is no severe valvular abnormality then you would expect normal life expectancy with proper care and secondary antibiotic prophylaxis. If there is severe valve involvement in the form of leakage and or stenosis (obstruction) then depends on that lesion. Your doctor would be more informed to give a more precise answer.