An assessment, as herein provided, may be made by the board at any time within five (5) years after any property owned, held or possessed, or alleged to have been so owned, held or possessed by any resident should have been returned by him for taxation, notwithstanding he shall have paid a tax assessed on the basis of returns previously made or filed, and notwithstanding the board shall have made previous assessments against such resident. In any such case, no credit shall be given for any penalty formerly assessed and paid.