Humans are not a dead end host for H5N1 at all. This is why there was such concern with the Egyptian clade, which had lower lethality and was primarily a pediatric form.
In fact, humans would be an ideal host for H5N1. With somewhere between 7-8 billion humans, we are a primary target for any opportunistic pathogen. And with a 7 day to 2 week incubation period, large collections of people would be like a flock of chickens, seemingly healthy, and by the next day, all dead or dying.
The five mutation barrier to humans just needs to be broken in the right place, like an urban area. Because it is a novel pathogen, it would take far less of it to cause an infection, a fraction of the amount of ordinary influenza.
And it has a far greater number of animal vectors than it typical, including those with very different immune systems.
The reason that I say that humans are a dead end host for the H5N1 virus is that it is still essentially a bird virus. The cell receptors that the H5 hemagglutinin binds, those with the alpha 2,3 sialic acid linkage, are only found in the lower respiratory tract in humans. Since the influenza virus can only transmit easily if it binds cells of the upper respiratory tract—those with the alpha 2,6 linkage—the H5N1 is almost non-communicable between humans. It is not transmitted through aerosols, but only through contact with infected fluids. Furthermore, because humans sick with H5N1 are kept in isolation, the virus has no chance to passage between humans, and thus has no selective pressure to make it H2H transmissible. Four of the mutations identified as necessary for H2H transmissibility affected H5 binding affinity. The other mutation affected one of the viral RNA polymerases (I forget which one), but this enables the virus to reproduce at a lower temperature, making it more suitable for growth in the human upper respiratory tract than in the bird gut.
For an H5N1 virus to spontaneously develop all 5 mutations in the course of a single human infection is possible, but highly unlikely. It would have to develop those mutations within the bird host—and since the mutations would make it less adapted to birds, those mutations would probably disappear soon after emerging.
The virus would be more likely to make the requisite mutations in a swine host, since swine have both alpha-2,3 and alpha-2,6 receptors in their trachea. I do not know to what extent H5N1 has affected pigs, if at all.
One last detail is that the tropism of the H5N1 for the lower respiratory tract is one of the factors making it so pathogenic. If the H5N1 were to develop tropism for the upper respiratory tract, it would cause less severe disease. This was observed in the ferret experiments done by Fouchier and Kawaoka.