Should I explain to the graduate admission committee why I am older than most prospective PhD students?

Such information would be relevant. The real trick would be to keep such a paragraph short and to the point. As such the question would be a good draft of such a section. I have two comments:

I would not start the second sentence with "as you know". If a committee member did not know, you make her or him feel ignorant. It is good to avoid invoking negative emotions in such a letter. Especially since leaving that part out does not change the meaning of the sentence.

It was not clear from the text whether it was the Bahai faith that prohibited it's members from going to university or whether it was the Iranian government that prohibited people with the Bahai religion to enter university.

I wish scaaahu had put that comment in an answer so that I could up-vote it.

Perhaps it will help you to know that I started the Ph.D. at age 56. It wasn't in a top ten university, but neither am I ashamed of my alma mater. Admissions committees are interested in potential for research and teaching. Show those and, with your background, you will get offers.

Do include a very brief explanation in either your cover letter or statement of purpose as scaaahu has suggested. It need not be as extensive as what you posted here. Just address the committee member who is thinking, "I wonder why...?" Something as simple as, "People of my faith are not allowed to study in university in my native Iran, so I got a late start."

I recommend that you put the information you gave us in your statement of purpose for a PhD application. At least for a US-style statement of purpose (which is usually about two pages) I would not suggest abridging the story you told us. Rather I agree with @scaaahu that your story is extremely compelling, much more so than what one normally reads in these kinds of statements.

If you can craft this as a narrative of the triumph of your intellectual interest and academic success over the adversities you've faced over a period of many years: look, that's awesome. If I saw that in a PhD application to my program (mathematics, UGA) then I would be passing your statement around for the entire admissions committee to read. If the other parts of your application were reasonably competitive, I would be well on my way to pushing strongly for your admission.

Let me end my saying that I was personally touched by your story. You have a lot to be proud of and will certainly serve as an inspiration to many others. Academia needs people like you.