(1) A child, his or her natural mother, or a man presumed to be his or her father pursuant to section 19-4-105 (1)(a), (1)(b), or (1)(c) or the state, the state department of human services, or a county department of human or social services, pursuant to article 13 or 13.5 of title 26 or article 5 of title 14 may bring an action:

(a) At any time for the purpose of declaring the existence of the father and child relationship presumed under section 19-4-105 (1)(a), (1)(b), or (1)(c); or

(b) For the purpose of declaring the nonexistence of the father and child relationship presumed under section 19-4-105 (1)(a), (1)(b), or (1)(c) only if the action is brought within a reasonable time after obtaining knowledge of relevant facts but in no event later than five years after the child's birth. After the presumption has been rebutted, paternity of the child by another man may be determined in the same action, if he has been made a party.

(2) Any interested party, including the state, the state department of human services, or a county department of human or social services, pursuant to article 13 or 13.5 of title 26 or article 5 of title 14 may bring an action at any time for the purpose of determining the existence or nonexistence of the father and child relationship presumed pursuant to section 19-4-105 (1)(d), (1)(e), or (1)(f).

(3) An action to determine the existence of the father and child relationship with respect to a child who has no presumed father pursuant to section 19-4-105 may be brought by the state, the state department of human services, a county department of human or social services, the child, the mother or personal representative of the child, the personal representative or a parent of the mother if the mother has died, a man alleged or alleging himself to be the father, or the personal representative or a parent of the alleged father if the alleged father has died or is a minor.

(4) Regardless of its terms, an agreement, other than an agreement approved by the courtin accordance with section 19-4-114 (2), between an alleged or presumed father and the mother or child does not bar an action under this section.