I've been practicing quite a lot lately, and 30-45 minutes is what I currently think of as a good session. But I can't do it every day. However on some of those days, I *can* practice for 5-10 minutes. How much of a difference will those 5-10 minutes make in terms of keeping my embouchure from getting lax?

Yes, Absolutely. You won't build stamina or flexibility but it will keep your muscle memory going; both in your lips and your fingers. I encourage my students to keep their horn out on a stand in a safe location so they can at least play a single chromatic scale each day.

Be sure to play whatever you do play with commitment and enjoyment. One scale, five minutes, any thing is better than nothing.

Any time spent practicing your horn is time well spent.

However, unless the other people living in your house are respectful enough not to handle your horn, I would advise putting your horn away every time you're done practicing. From my own experience: in the past a few of my things (not my horn, thankfully) have been damaged at the hands of my siblings.