Praise be to Allah.
The conditions for speaking to a woman to whom one is not related are mentioned in the following aayaat (interpretation of the meaning):
". . . And when you ask (his wives) for anything you want, ask them from behind a screen; that is purer for your hearts and for their hearts . . ." [al-Ahzaab 33:53]
". . . then be not soft in speech, lest he in whose heart is a disease should be moved with desire, but speak in an honourable manner." [al-Ahzaab 33:32]
Ibn Katheer, may Allaah have mercy on him, said in his Tafseer: "This means that they should not speak softly. Allaah commanded them to speak in a concise and decisive manner (i.e., they should be serious and brief in their speech, and not be vague or talk aimlessly). There should be no possible indication on the face that could be taken to indicate any softness in the heart, as the Arab women (before Islaam) used to do when speaking to men, by making their voices soft like women who are taking care of small children, or like prostitutes. Allaah forbade women to do that.
The phrase "lest he in whose heart is a disease should be moved with desire" means lest such a person should hope for immoral deeds, indecency or romance. "Speaking in an honourable manner" means speaking in a way that does not go against Sharee’ah or offend people. Women are encouraged when speaking to men to whom they are not related and to mahrams among their in-laws to be somewhat rough or abrupt in their speech, without raising the voice, because they are commanded to lower their voice.
Speaking with a woman to whom one is not related (i.e., not mahram) should only be for a specific need, such as asking a question, buying or selling, asking about the head of the household, and so on. Such conversations should be brief, with nothing doubtful in either what is said or how it is said.
The idea of limiting speech with women to the five instances mentioned in the question needs to be approached with caution, because they could be taken as examples instead of limits. One must also adhere to the conditions set out by the Sharee’ah even in instances where such conversations are necessary, such as in da’wah, giving fatwas, buying or selling, etc. And Allaah knows best.