The executor of every will and the administrator of every estate, at the time of filing with the register of wills or clerk of the orphans' court the inventory and appraisal of such estate, shall file with such register of wills or clerk of the orphans' court a statement in duplicate, under oath or affirmation, setting forth the items included in such inventory and appraisal which may be liable to the tax imposed by this act. The register or clerk with whom the same is filed shall forthwith send one copy thereof to the board. It shall be the duty of the board to proceed at once to assess the tax due from such decedent, with interest, as provided in this act. Such assessment shall include all property owned, held or possessed by the decedent which should have been returned by him for taxation for any former year or years, not exceeding five (5) years. In any case where a false, incomplete, incorrect or inaccurate return has been previously filed, the board shall make an additional assessment for the five (5) years immediately preceding the year of assessment, in the same manner as otherwise provided in this act. The school district levying the tax may proceed to collect the said tax by presenting a claim therefor to the orphans' court of the proper county, or may proceed by action or suit at law in any court of competent jurisdiction, or take any and all other appropriate steps or procedure for the collection of such taxes.