If from any cause any municipality fails to collect the whole or any portion of any special assessment or special tax which may be levied, which is not canceled or set aside by the order of any court, for any public improvement authorized to be made and paid for by a special assessment or a special tax, the corporate authorities, at any time within 5 years after the confirmation of the original assessment, may direct a new assessment to be made upon the delinquent property for the amount of the deficiency and interest thereon from the date of the original assessment, which assessment shall be made, as nearly as may be, in the same manner as is prescribed in this Division 2 for the first assessment. In all cases where partial payments have been made on such former assessments, they shall be credited or allowed on the new assessment to the property for which they were made, so that the assessment shall be equal and impartial in its results. If this new assessment proves insufficient, either in whole or in part, the corporate authorities, at any time within the specified period of 5 years, may order a third to be levied, and so on in the same manner and for the same purpose. It shall constitute no legal objection to any new assessment that the property may have changed hands, or been encumbered subsequent to the date of the original assessment.