Medical Malpractice Relief Act of 2005 - Amends the Internal Revenue Code to allow a business tax credit for taxable years beginning in 2005 or 2006 for expenditures for medical professional malpractice insurance. Allows a credit for: (1) 30 percent of the malpractice insurance expenditures of a physician who practices in any surgical specialty or subspecialty, emergency medicine, obstetrics, or anesthesiology or who does intervention work that is reflected in medical malpractice insurance expenditures; and (2) 20 percent of such expenditures of a physician who practices in general medicine, allergy, dermatology, pathology, or other specialty and of any hospital, clinic, or long-term care provider. Limits the amount of expenditures that may be taken into account to twice the average of costs of medical malpractice insurance for similarly situated health care providers. Directs the Secretary of Health and Human Services, acting through the Administrator of the Health Resources and Services Administration, to make grants to certain nonprofit hospitals, clinics, and long-term care providers to assist such entities in defraying their medical malpractice insurance expenditures. Limits the amount of such grants to 15 percent of the medical malpractice insurance expenditures incurred by such entities in any year.
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