I am US Permanent resident, My wife is British, and she got a 5 yr multiple tourist visa. Can she use it?

Well, considering that if you filed an immigrant petition for your wife it would take 5 years before it became valid for use, some folks would be inclined to get around that by using a tourist visa to try to live in the US while they were waiting. Interesting that you haven't filed as of yet. Most folks want to live with their spouses, which is why lots of others have abused their visas in the past. If it appears your wife is using a tourist visa to live in the US, that she's spending more time here than there, they could revoke the visa, so take care with that. Under the law, they don't need absolute proof to find someone inadmissible.

We can refuse her application for admittance if we (CBPO's) feel that she does not have adequate ties to her home country. She needs to prove (yes she must prove) that she has a home to go back to, she needs a firm date return ticket, she needs to have adequate funds to support herself while here, that she has employment to return to, etc.

All a visa is, is a document that the alien has the right to apply for admission to the United States, no the right to enter.

Being that she is visiting her spouse, we will have a hard time believing that she is not coming to the United States to immigrate without an immigrant visa.

Why have you not applied for her to immigrate as the spouse of a LRP?

They can stop her from entering the United States for any reason which they see fit (I can think of plenty just off the top of my head).

NB: The only people who have the right to enter the U.S. freely are U.S. citizens, anyone else can be refused entry for pretty much any reason. Your wife should bring plenty of evidence and supporting documentation to prove her ties to the U.K.