how come a person can only increase oxygen levels in the body by 3-5%?

Your body has a gradient for exchange of Oxygen, when you hyperventilate you mess up that gradient.
Think of when you stink up one part of the house, the stink will naturally go to the nonstinky part of the house, that's a gradient, and it's very easy to stink up the rest of the house. However, once the whole house is stinky, it's really hard to force the stink into one particular spot. It's the same way with oxygen, if there's no gradient between your blood and the air in your lungs, it's really hard for the transfer to take place to increase oxygen levels more. Therefore as more oxygen gets in the blood, the harder it is to get *more* oxygen in the blood.

In addition your body has a fairly narrow tolerance so you pass out before you manage to get any more oxygen in.