Rabbi Blech says the Earth is billions of years old because Torah says G_d created the world in six 'periods' or phases not actual Earth 'days'.
Modern man with free will is only 6,000 years old even though humanoid creatures existed before then.
This makes sense. It was 6 days from G-d's perspective in the center of the universe. Time is relative to where it's measured from. On earth it may have seemed like millions of years but from the center of the universe only 6 days.
That's pretty much what Dr. Schroeder postulates.
Schroeder stipulates that Genesis should be interpreted as if there are TWO biblical clocks at work.
The first clock begins ticking when Hashem creates the Universe.
Time on this clock is measured from Hashem's perspective looking forward. Yes, the term 'day' is used (the Rambam even specifically states that a 'day' consists of 24 'hours') to quantify time as measured by this clock. However, it's important to note and essential to understand that the first 6 'days' as depicted in Genesis is not written from a human perspective. It can not be taken literally in it's entirety and is certainly partly written in parable form. This view is supported not only by the Rambam, but also the Ramban, Kabbalists, and other sages.
A separate, second clock begins ticking when Hashem creates Adam's soul and from that point on time is measured in understandable human terms looking backwards. Using the two clock hypothesis (which was not originally advanced by Schroeder, he's merely repeating what our sages taught us centuries ago) in conjunction with modern scientific knowledge, the age of the Universe can be determined to be approximately 15.75 billion years.
So obviously the Torah is correct, and the apparent conflict of 5765 versus 15.75 billion easily resolved.