Your question was not about introducing the topic to children, but about what is correct, or how they are "usually" read.
Moreover, "two fives and one" is not a way of reading, but a way to describe the meaning. Each has its place. I would say that in the same contexts in which I might say "two tens and one" in place of "twenty-one" -- that is, only in discussing what "21" means, not in reading it aloud. Yes, it's a good idea in some situations, but it isn't the answer to "how is it usually read aloud".
Yes, it doesn't take me long to climb onto my hobby horse, which is the lamentable ways elementary math is being taught, starting with the essential skill of counting. I should have perhaps simply expressed my gratitude for the information and moved on. I was checking to see if what I suspected was correct, which is that the usual terms are not the proper ones, and that children are not being taught how to count properly in any base, except for Chinese, Japanese, Korean and Welsh-speaking children who have the benefit of being taught base-ten counting, in addition to various traditional forms.
When reading numbers in vernacular English 11 is read as eleven. When reading numbers using base-ten, 11 is read as "one ten and one", or "a ten and one", or "ten and one". As you point out, that explains the numbers, which is of course the reason they should be used. But it only matters at the very beginning. Telling seven and eight year olds that eleven can also be called ten and one is way too late. They should learn that as soon as they can count to ten.
It might rankle to learn that you've been doing something wrong for years, but I can only offer the defence that it's the simple truth. Since the counting sequence in base-ten counting is ".... nine, ten, ten and one" etc, the counting sequence in base-five must be ".... four, five, five and one," and so on. Of course other words may be used, but for beginners that must be the best and clearest way to go
I really hope my style, or lack of, doesn't set you against me. As I see it, math education produces perhaps nine math-averse school graduates for every math-confident one. There is massive room for improvement, and the most glaring example is counting, which can be fixed overnight, for free. Any Korean five-year old can teach younger sibs and playmates how to count to a hundred in a few minutes, and they themselves probably learnt it the same way, from other children, and that's because they have to proper tools to do it.
In contrast I read something recently about a new initiative which might see US children being able to count to 20 by the time they start school. Now that's just sad.
All it takes is for pre-school teachers to teach base-ten counting, which requires no permission from parents, no training, no books and no more instruction than could be contained in a couple of tweets. Frankly I wouldn't waste time on also teaching them the vernacular sequence: better for them to learn that for themselves, which they will easily do, and by so doing they will own it. Better to get out of the way.
And yet the considered opinion of experts, such as Stanislas Dehaene in "The Number Sense", is that introducing base-ten counting is impossible. That's because they wrongly presume that doing so would mean abolishing the vernacular counting sequence, which would indeed be impossible.But as the Welsh example shows, base-ten counting can be introduced without any opposition or trouble, and Welsh-speakers today freely use their traditional counting numbers and base-ten, depending on the situation.
Hmm, here I am again, on a soap-box, riding my hobby horse OT. Better stop now or I'll start getting the dreaded TLDR.