Let me explain why #2 is correct but #3 is wrong. In #2, "death" is the object of the preposition "after": "after her death". That makes sense. In #3, "death" is STILL the intended object of the preposition (because you still mean "after her death") but the sentence is written in such a way that it appears that "five years" is the object of the preposition. This confuses the listener. When you say "I met him after five years", I start to wonder "after five years of what?"

3 is wrong but both 1 and 3 both might overemphasize the wife by making her the sentence subject. You can say: I met him in 2005, five years after his wife’s passing. (Keeping the focus of 2 but with the information and tone of 1 and 3)

1. and 2. are good. 3. is not very good. It may not seem to make much sense, but you could say, "His wife passed away in 2000. I met him five year after." (basically the same as later.--but 1. is still probably better).