Why aren't there 5 Noble Truths? Consider the fact that our Nirvana depends on one crucial truth and that is law of Karma. Good karma bear good fruit and bad karma generates bad results. 

Why didn't Buddha say that Fifth Noble Truth is law of Karma ?
Other answers say that kamma is already covered by, or implicit in, the first and/or second noble truths.

I think it's related to the fourth noble truth -- i.e. you say that kamma is important to attaining nirvana (and I think that "the path towards attaining nirvana" is what the fourth noble truth is about).

Or, perhaps, you can see "bad karma" and "good karma" in the second and third noble truths respectively.



I find the logical structure of the four noble truths satisfying or persuasive.

The first three have the structure of a syllogism:


premise: dukkha exists, and is this and that
premise: dukkha is associated with craving
theorem: dukkha ceases when craving ceases


So that's the doctrine "in a nutshell".

The fourth is, then, an introduction to the rest of Buddhism:


to begin to implement that in practice, see the noble eightfold way




I think that (as well as karma) there are other important aspects of dharma -- e.g. anatta, dependent origination, the sangha, the qualities conducive to Enlightenment, and so on.

So I don't see why you see the need to "privilege" karma (as more important than other doctrines) -- but it's helpful that there is a doctrine with only 4 (memorable) truths, rather than (less memorable) 20. The "4 truths" served as (and still serve as) an introduction to the dharma.



Or perhaps you're saying that the doctrine of karma should be privileged because it's the single most important doctrine to remember. If so, maybe you're not wrong; but there are also some other dharmas that people have been inclined to say are the most important -- for example, "right view"; or maybe "harmlessness", "generosity", "skilful virtue", "admirable friendship", "attention"; and so on.