is it legal to double the price on an item because there are only two left?

In this case yes. In other cases, no.

You can not double the price of gasoline just because there is a shortage.

You can "reprice" an existing item on a store shelf however.

the shopowner is an idiot to risk losing your business forever, for $5 however.

It's extremely unethical, and could be illegal.

If the price tag is on the item and says $5 each, then legally it's a gray area. If it was an honest mistake where another customer accidentally put the book back in the wrong place (like a $5 bin/shelf), or an employee accidentally priced it wrong, then most businesses will honor the price, and fix the problem so it doesn't happen again. If the business doesn't want to honor it, then the customer could sue, or press charges for false advertisement. They may not win, but it's a possibility.

It's also possible that the customer could sue for discrimination, if she felt she was being discriminated against for some reason that's protected such as age, gender, race, etc.

Yes, they can. And the customer has the right to refuse to purchase the book from that store and find a copy somewhere else for a lower price.

yes its the business that purchased the item to start with. Its best to look on the Web if that happens to see whom else has the same thing with all the information one can find quickly on their now.

This is supply and demand affecting prices. It is perfectly acceptable. You don't have to buy it from that seller. If he is the only seller who has those books, as a seller he gets to set the prices.

Yes.

it's called supply and demand, yes