You don't need punctuation at the end of a bullet point if the bullet points themselves are sentence fragments, rather than full sentences.
The problem is, the first two entries in your examples are not grammatically appropriate sentence fragments. If you put up a sign saying "No older than 5 years," the punctuation is not going to be what makes people see the sign as ungrammatical. You need to rephrase that somehow: "No children over five" or "Children 4 and younger only" or even, at a pinch, "4 and under only".
Also, do not capitalize "Hair."