Yes, you can deduct the full $5,996 you paid in interest on the refinanced loan as long as the additional funds borrowed were used to improve the house. If the additional money you borrowed was used to pay off other debt or for other personal reasons then part of the interest you paid is not deductible.
Please go back through the mortgage section of TurboTax and review your answers to the questions to verify that you answered them correctly.
Link about Mortgage Refinance Deductions
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