Section 5C. With respect to each parcel of real property classified as Class One, residential, in each city or town certified by the commissioner to be assessing all property at its full and fair cash valuation, and at the option of the board of selectmen or mayor, with the approval of the city council, as the case may be, there shall be an exemption equal to not more than 35 per cent of the average assessed value of all Class One, residential, parcels within such city or town; provided, however, that such an exemption shall be applied only to the principal residence of a taxpayer as used by the taxpayer for income tax purposes. This exemption shall be in addition to any exemptions allowable under section five; provided, however, that in no instance shall the taxable valuation of such property after all applicable exemptions be reduced below ten per cent of its full and fair cash valuation, except through the applicability of clause Eighteenth of section five. Where, under the provisions of section five, the exemption is based upon an amount of tax rather than on valuation, the reduction of taxable valuation for purposes of the preceding sentence shall be computed by dividing the said amount of tax by the residential class tax rate of the city or town and multiplying the result by one thousand dollars. For purposes of this paragraph, ''parcel'' shall mean a unit of real property as defined by the assessors in accordance with the deed for such property and shall include a condominium unit.

In those cities and towns in which an exemption is made available hereunder, a taxpayer aggrieved by the failure to receive such residential exemption may apply for such residential exemption to the assessors, in writing, on a form approved by the commissioner, on or before the deadline for an application for exemption under section 59.

A timely application filed hereunder shall, for the purposes of this chapter, be treated as a timely filed application pursuant to section fifty-nine.

For purposes of this section, with respect to real property owned by a cooperative corporation, as defined in section 4 of chapter 157B, that portion which is occupied by a member pursuant to a proprietary lease as such member's domicile and is used as such member's principal residence for income tax purposes shall be deemed to be real property owned by such member for purposes of this section, provided that the portion of the real estate is represented by the member's share or shares of stock in the cooperative corporation and the percentage of such portion to the whole is the percentage of such member's shares in the cooperative corporation to the total outstanding stock of the corporation, including shares owned by the corporation. Such portion of such real property shall be eligible for exemption from taxation pursuant to this section if such member meets all requirements for such exemption. Any exemption so provided shall reduce the taxable valuation of the real property owned by the cooperative corporation; provided, however, that the reduction in taxes realized thereby shall be credited by the cooperative corporation against the amount of such taxes otherwise payable by or chargeable to such member. Nothing in this paragraph shall be construed to affect the tax status of any manufactured home or mobile home under this chapter, but shall apply to the land on which such manufactured home or mobile home is located if all other requirements of this paragraph are met. This paragraph shall take effect in a city or town upon its acceptance by the city or town.