A court of this state may exercise personal jurisdiction over any nonresident or his executor or administrator, as to a cause of action arising from any of the acts, omissions, ownership, use, or possession enumerated in this Code section, in the same manner as if he were a resident of the state, if in person or through an agent, he:

(1) Transacts any business within this state;

(2) Commits a tortious act or omission within this state, except as to a cause of action for defamation of character arising from the act;

(3) Commits a tortious injury in this state caused by an act or omission outside this state if the tort-feasor regularly does or solicits business, or engages in any other persistent course of conduct, or derives substantial revenue from goods used or consumed or services rendered in this state;

(4) Owns, uses, or possesses any real property situated within this state; or

(5) With respect to proceedings for alimony, child support, or division of property in connection with an action for divorce or with respect to an independent action for support of dependents, maintains a matrimonial domicile in this state at the time of the commencement of this action or, if the defendant resided in this state preceding the commencement of the action, whether cohabiting during that time or not. This paragraph shall not change the residency requirement for filing an action for divorce.