Who told you it was too close?

It was an exterminator I had hired..... hardly an expert on this!

Ok, so my advice is just intended to be my personal opinion so take it as that. Your stem wall looks great and goes down a ways and it is at a corner where I presume there's no plumbing. It's fine. Roots of a yucca like that won't heave a house. If it was a huge, invasive root tree going after water it would be different. Or if you had stem wall deterioration, you should worry but at that point your yucca would be the least of your problems. So, just keep an eye on it (and the rest of your stem wall, you should walk it monthly) and pull out the plant if you notice any issues. Oh, and don't water it so water pools all around the foundation, water should run away from the house.

Termites are drawn to moisture, not surprisingly, and your exterminator told you it is too close to your house because any plant that close to your house is a source of potential moisture that can attract termites. That said, you have an Agave there, not a Yucca, and that is too large a plant for that spot so close to your house. That said, other than possibly attracting termites, it shouldn't cause any harm.

An Agave! OK, I am learning a lot.... I just moved to AZ, so I am reliant on others for my plant knowledge. The exterminator did not say anything about the plant attracting termites (although I can understand that), he specifically said the danger is from the roots heaving the concrete. I will monitor everything very carefully - including keeping a watchful eye for termites. But I am relieved that it will probably not cause any structural damage to my house. Thank you for all the great responses!

Lol, did not catch it was an agave, too busy looking at the house!

Arizona has subterrainian termites and they make little mud tubes up your stem wall. Google images for that type of termite so you know what to look for when you do your monthly walk. I know it sounds weird to walk your foundation perimeter once a month but that's how you catch issues before they get out of hand. I don't know how many major slow leaks and termite infestations I've seen that could have been detected before they caused major damage if someone had just looked at the house regularly and investigated when stuff looked different the next time they saw it.

That is a mature agave, it's been there a long time. If it was going to cause problems, I'm pretty sure it would have already done so.

Thanks again everyone!

Probably too late for this post, but I just want to warn everyone when pruning or trimming agave. Recently, I trimmed mine and was struck in the palm with a tip (then I went to get my gloves...silly me....) and within two hours my hand swelled and was rendered useless. Bending my fingers was excruciatingly painful! Urgent care doc told me Agave can be cruel and gave me prednisone and hydrocortisone cream, which works wonders! Most people on the web discuss itchy rashes, so beware- rash or inflammation, there's no need if you properly suit up to wrestle these beautiful beasts! And now we all know :)

Not a yukka - defintiely an agave