OK, lets get something straight here. Real world results are much different than the size of a hole on a paper target. The 5.56 mm round has excellent ballistic properties for what is was designed for. That is, to engage a target out to roughly 400 meters, in a rifle with a barrel length of 14.5 inches or greater. Below a 14.5 inch barrel, the round will lose the necessary velocity to effectively engage a target out to the range that the round was designed for. However, at closer range, it will still have over three times the energy of a .45 ACP round.
However, more important than the energy delivered by the round, is what happens to the round when it enters the target....
A standard FMJ handgun round will enter the body, and barring striking a bone, it will continue into the target until all of its energy is depleted. This will cause one wound channel. Any soft tissue, blood vessel or organ damage will start the process of internal bleeding. Handgun rounds are inherently stable rounds in both low drag, low viscosity and high drag, high viscosity environments, and generally do not spall (tumble) within the body, as they simply lack the velocity and inherent instability in more viscous environments (aka: in the body) to do so.
A 5.56 mm round is an inherently stable round in low drag, low voscosity environments (aka: air), but is inherently unstable in high drag, high viscosity environments. What this means is that once the round has entered the body, it's inherent instability will cause it to spall, or tumble, once it has entered the body and penetrated a number of centimeters into soft tissue. That, coupled with its extreme velocity, causes a massive shockwave within the body, damaging blood vessels, soft tissue, and organs FAR outside the diameter of the initial wound channel.
As I said before, I have PERSONALLY seen the effects of both handgun rounds and rifle rounds on human beings. Both in combat situations, as well as in post mortem autopsys. Rifle rounds, in almost 100% of situations, cause massive internal injuries, far in excess of what a handgun will cause, simply because of the facts outlined in the above two paragraphs.
Extrapolating these results to an animal with the bone density and white adipose tissue depth of a bear, means that a handgun round will most certainly fail to kill a bear, as it will fail to penetrate these substances, barring extraordinary circumstances.
If you want to talk about terminal ballistic properties of various rounds, I would be more than happy to indulge. However, as I said before, barring extraordinary circumstances, shooting a bear with a handgun will just piss it off.
Can it be done? Yes. Is it likely? Hell no!
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