Every good law is first a good teacher and last a good protector.
The seven Noahide laws are the very basics provided to the roots of humanity according to the Torah. Within them linger the secrets of existence. Regardless as to how close you come to discover the Truth, those laws will not lose validity nor purpose.
Manly P. Hall once talked about the curious phenomenon of 5 versus 7, which somehow represent a pattern found throughout all of antiquity, regardless which culture. This same pattern can be found in those 7 laws as the last 2 of them are in some way only an elaboration and could be redundant, if the first 5 were fully understood.
I yet have to examine the associations to the Sephirot on the Tree of Life according to Kabbalah, but they do seem interesting enough to list them as well.
1) Do not worship idols [Netzach "eternity"]
Meaning: Do not separate yourself from the Oneness of all within the Creator. Recognize and keep in mind that we are all one at the core of existence to which we owe everything and for which we exist. Violate this and the roots of strive break our ground.
2) Do Not Curse The Creator [Hod "splendor"]
Meaning: Everything you say is of great power. Say something bad and you curse the Creator. Lie and you curse the Creator. Speak too soon and you might curse the Creator. In essence this means, words have tremendous value, be caring and loving with your use of them.
3) Do Not Murder [Gevurah "severity"]
Meaning: Life is given to all by the Creator. You have to recognize the holiness of Life. Break it anywhere and you break it from yourself and you break it from all. We are not given the ability to judge about who or what is to live or not. (Murder = unlawful killing. Which acknowledges the potential killing as the result of defense, accident or- most controversial- ruling.)
4) Do Not Steal [Tiferet "beauty"]
Meaning: Do not take away from anybody that which is not yours. Respect the property of others, for you can only know what is yours by what you have earned yourself. Also, our society has to rely on trust. Break this trust and you break society.
5) Do Not Be Sexually Immoral [Cheset "loving kindness"]
Meaning: Love and care for your family at all times. Do not harm the divine purpose of having a family.
6) Do Not Eat A Limb Removed From A Live Animal (3rd law elaborated) [Yesod "foundation"]
Meaning: The 3rd law not to murder was for more than just humans amongst humans, but the sixth law tries to make clear that life has to be respected in every way. One need not murder a being to violate divine law. Harming it is already a transgression. Every living thing is given a soul and every soul is subject to spiritual evolution. Harm it at an early point and it will carry over.
7) Set Up Courts Of Justice (4th and 5th law elaborated) [Malkhut "kingship"]
Meaning: Guide the multitude of humanity as it is meant to grow. But growth brings challenges of all kind. Deal with those challenges by means of a system that upholds morals and provides justice. This justice provides trust amongst humanity and reliable guidance.
The Sephirot associations also hint at the 5 versus 7 pattern, as the core of the tree is contained in the first 5 laws, while the last 2 are the transformation of them into our physical manifestation. It feels a little bit like reaching at first, but it also feels inspiring to contemplate further about it.