Resident Physician Shortage Reduction Act of 2019 This bill increases the number of residency positions eligible for graduate medical education payments under Medicare for qualifying hospitals, with an aggregate increase of 3,000 positions per fiscal year for five years. Of these positions, at least 1,500 per fiscal year must be for residents in a shortage specialty residency program (i.e., a program in a specialty in which baseline physician requirements projections exceed the projected supply of total active physicians, as identified by the Health Resources and Services Administration in a specified report).