Lohman446 said:
May I ask the formula that argues 5 is not enough and 8 is?
There's no easy answer to that question, but it's easier to answer THAT question than to answer why you think you'll never be able to use more than 3-5 rounds in any situation you are likely to face.
Carrying a weapon can be seen as a form of insurance: you hope you'll never use it, but you have that insurance because it's a possibility you want to be ready for. I agree that it's hard to come up with a good rationale to justify why 5 rounds is insufficient and 8 rounds isn't. But...
IF the attacker is close and has a firearm and you've not got your weapon in hand:
The number of rounds will likely be irrelevant. And whether you act or surrender will be depend on variables we can't really know. (I've read of a number of such "confrontations" where armed victims simply gave up their wallets and valuables, but never attempted to use their weapons.)
If the attacker is on you and you have had time to get your weapon out and ready:
The number of rounds may be less relevant than retaining your weapon for actual use. If you can control your weapon, and the attacker does not have a firearm, 5 rounds may be enough to gravely damage the attacker- - as many may be contact hits -- but the attacker can still do you harm. But 8 rounds may not greatly change the outcome unless you're able to make a central nervous system hit.
If the attacker is more distant, and you are able to access your weapon and are ready to use it:
The number of rounds available may be very important, as it's foolish to assume that the first couple of rounds you fire will be hits, or if hits, that the shots will deter or stop the attack. It is likewise foolish to assume that the attack will be over in a minute or less. Even if the shots fired are good hits your attacker, even if badly or mortally wounded may still be still able continue the attack if you're not able to stop it quickly. I have seen many discussions of that happening.
For me, it's not just a question of how many rounds are best, but whether the extra rounds have the potential to be useful in situations we aren't likely to predict.
I consider whether I carry a weapon and whether the weapon carried uses 5, 10, or 15 rounds a form of INSURANCE. While I might err in these "insurance" choices I will try to err on the side of a few more rounds, and on the side of a the largest caliber weapon I shoot well.
If I'm wrong in my decisions and don't survive (or otherwise lose in) a self-defense conflict, the extra extra rounds available and my weapon choice will be irrelevant.
If I survive, it may be because of those the extra rounds, even if not used, were an important part of my potential defense that helped me maintain the necessary mindset leading to a successful outcome.