This diagrams to:

laws → crimes

That doesn't follow from the principle in the stimulus. If we consider the contrapositive of that principle (crimes → laws), we'll see that this answer choice actually confuses the necessary and sufficient conditions. So (A) is incorrect.

This diagrams to:

/crimes → /laws

This confuses the necessary and sufficient conditions from the principle in the stimulus. So (B) is incorrect.

The discussion of what "many" means for conditional logic will be more relevant for (E). For (C), notice that even if we diagram this out "as is," the direction of the logic between "laws" and "crimes" is still incorrect:

many laws → many crimes

The principle we drew above, with its contrapositive, doesn't let us draw any conclusions that look like this: we can't start with the presence of any laws and conclude anything about the presence of any crimes. We can only say that if there are no laws, there are no crimes. And so if knowing that there is any amount of laws still doesn't let us conclude anything about any amount of crimes, knowing that there are "many" laws certainly won't let us conclude that there are "many" crimes. So (C) is incorrect.

Correct. This is a very tricky answer choice, because the "some" might make you think we are dealing with the logic of intersecting sets. But "some" here is actually interchangeable with "any." Remember that "some," on the LSAT, means "at least one" and has no upper limit: in other words, any amount, as opposed to no amount or none. So what (D) is saying is that a society with any amount of crimes must have at least one law. But this says the same thing as the contrapositive of the principle in the stimulus, which didn't specify an amount of crimes or an amount of laws. It only said that if there are crimes, there must be laws; the presence of crimes (any amount) guarantees the presence of some amount of laws:

crimes → laws

Because it rephrases the contrapositive of the principle in the stimulus, (D) is a valid inference.

Unlike (C), (E) actually gets the general direction of the logic right: we infer the presence of laws from the presence of crimes, as the contrapositive of the principle in the stimulus does. The problem is that it tries to be too specific: it insists that the presence of "many" crimes is an indicator of "many" laws:

many crimes → many laws

Notice that this is much more specific than what we can infer from the stimulus. The contrapositive of the principle in the stimulus just tells us that if there are (any) crimes, then there must be (some amount of) laws:

crimes → laws

But this doesn't specify a specific amount of either crimes or laws. By this principle, it could be true that even if there are few crimes, there are many laws, or even if there are many crimes, there are only a few laws (maybe there aren't many laws, but people break them all the time). The fact that this principle is about indeterminate amounts is why it can be expressed with "some," as in (D). But "many" is too specific, so (E) does not necessarily have to be true.