"Zoonotic" is generally a term for a disease readily transmissible to humans or a disease that has a very similar human counterpart, and often that does not transmit readily from person to person -- though obviously there are a lot of exceptions, my definition is only a generalization.

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That said H5N1 does seem to be general enough that it can infect a wide variety of warm-blooded organisms, and to spread between many (though not all) of those species without birds - and that is very disturbing, because we know only one of two critical facts about H5N1 in people:

• We know we can get it, a number of people in close contact with birds have come down with it. I'm talking people who clean coops (read: barns) in chicken farms and that kind of thing, not a person with a bird feeder on their balcony.
• We don't know what keeps it from spreading from person to person. It can get you sick enough to need a hospital, if not kill you, but for whatever reason an ill person is not (yet) contagious to other humans. But it can spread in other mammals, eg. from one mink to another. Are we just not dense enough (population wise), the mink farm was loads of them all in an enclosure in constant close contact. Or a time factor, like it takes hours to acquire the load needed to trigger an infection, and the few minutes of contact human to human is not enough? Or is it biological, eg. it can't hijack the reproduction mechanics necessary to reach the level where it would be contagious? Or something else? We don't know, and considering how severe of a disease this is that is very troubling.

edit: to be clear, there are some solid information/fact-based hypotheses that posit why it may not be human-human transmissable (see the rest of this thread), but we don't know which one or perhaps some/all the possible reasons are the 'correct' ones; this is ELI5 not ELIdoctor