In comments on my previous post, an interesting question was raised, "Why do you take his word for it?". While I didn't post the full article or the thoughts that brought, in light of that question, I think it's important to add to what I posted previously...
(more from Daniel Pipes...)
The subsequent 60 years, however, witnessed a resurgence of the Orthodox element. This was, again, due to many factors, especially a tendency among the non-Orthodox to marry non-Jews and have fewer children. Recent figures on America published by the National Jewish Population Survey also point in this direction. The Orthodox proportion of American synagogue members, for example, went from 11% in 1971 to 16% in 1990 to 21% in 2000-01. (In absolute numbers, it bears noting, the American Jewish population went steadily down during these decades.)
Talking about the 5% figure, it seems pretty reasonable and matches most other info I've read that most of American Jews and most of the population in the Yishuv (pre-Israel-nationhood Jewish settlement in Israel) was minimally observant and not sending their children to Torah based education institutions (which were pretty much non-existant outside of Europe pre-World War 2).
The percentage of the Jewish population that is religiously observant is growing, and the pace of growth is also growing, both because of birth-rate (large family sizes) and because of outreach efforts. Though I have no official statistics, I've heard and personally seen that yeshiva's are larger than they have been in hundreds of years, and the largest yeshiva's (Mir & Ponevetz for example) are 5 times larger than they were before World War 2. Further, the percentage of the religious jewish population that is engaged in full time Torah study is also at a (seemily) all time high.
There are, of course, a number of enabling factors making this possible. The tremendous relative wealth increase of the Western world (including Israel), where probably over 98% of the world jewish population resides versus the 18th century (for example), allows the jewish community to focus a significant amount of resources beyond direct survival needs.
The story, however, of how the religious jewish community got from a post-World War 2 precipice to the stable and strongly growing position of today is a cloaked miracle and an amazing statement of complete life long dedication and effort by both the selfless leaders of the generation and the communal focus on what's truly important.