(a) Any owner of real estate located in the district, at any time within five (5) days from the giving of the notice, may appeal from the action of the board of assessors in readjusting or refusing to readjust the assessment against his property by filing with the clerk, in writing, his notice of appeal from the action of the board of assessors.
(b) The appeal shall be heard and disposed of at the next meeting of the city council.
(c) The city council shall enter upon its minutes the result of its findings on the appeal and shall have a copy of its findings certified to the board of assessors who shall make their assessment conform thereto if any change has been made therein by the council.
(d) Any person who shall fail to begin legal proceedings for the purpose of correcting or invalidating the readjustment or any new assessment against his property within thirty (30) days from the publication of the notice provided for in § 14-218-123 shall be forever barred and precluded.