There is an interesting coincidence at work: 5 Gyr is remarkably close to the 10 Gyr lifetime of main sequence stars (and to the 14 Gyr age of the universe). This is unexpected, as evolution proceeds by molecular processes and natural selection among complex organisms, whereas stellar lifetimes are determined by nuclear physics.
If T were much smaller than 5 Gyr then it would be improbable for evolution to have been so slow on Earth.
It seems more plausible that T is much larger than 5 Gyr, in which case we were lucky, in a sense I will explain. Inflationary cosmology predicts a very large universe (much larger than what is currently visible to us), so that complex life is likely to exist somewhere in the universe. Conditioning on our own existence (a use of the weak anthropic principle), we should not be surprised to find ourselves lucky – the few Earth-like planets that manage to evolve life must do so before their suns die. Intelligent beings, while not likely to evolve on any particular Earth-like planet, are likely to observe an evolutionary history that took place over a fraction of 10 Gyr.
Why should T be so large? At present we are unable to make quantitative estimates for the rate of evolution from first principles. It is entirely possible that certain evolutionary steps were highly improbable, such as the appearance of the first self-replicating complex molecules. One can also imagine abstract fitness surfaces with local maxima that trap the system for exponentially long periods of time.
I would not be surprised to find that T is exponentially larger than 5 Gyr. Godel went so far as to propose: “… a mathematical theorem to the effect that the formation within geological times of a human body by the laws of physics (or any other law of a similar nature) starting from a random distribution of the elementary particles and the field, is about as unlikely as the separation by chance of the atmosphere into its components.”
The framework described above makes the following predictions:
1. The overwhelming majority of Earth-like planets are devoid of life, thereby resolving the Fermi Paradox.
2. Improved understanding of evolution will uncover highly improbable steps – that is, improbable even over billions (or perhaps 10^100 !) of years. The fact that life on Earth climbed these steps might suggest intelligent design or divine intervention, but is better explained by the anthropic principle.
See related post evolutionary time scales.
Note added: This idea came to me after reading some discussion of ID and the question of improbable steps in evolution. (Here improbable means, for example, that even in an Earth-size population the multiple simultaneous mutations required jump across a particular fitness valley are unlikely to occur in 5 Gyr given the known mutation rate.) It occurred to me that under certain assumptions what might appear to be ID could actually be due to selection bias – not taking into account the possibility that complex life is rare even on Earth-like planets. It turns out that the idea is not new – it goes all the way back to Brandon Carter’s 1983 paper which (I believe) coined the term “anthropic principle”! See John D. Barrow and Frank J. Tipler, The Anthropic Cosmological Principle, p. 557 for more. Also see this 1998 paper by Robin Hanson (thanks to a commenter for pointing it out). If one assumes many improbable required steps, one can deduce an upper estimate on the remaining time over which favorable conditions can persist on Earth. Note it appears the remaining lifetime of the sun is less than 1 Gyr, so the coincidence is tighter than I suggested in the original post. As the number of required improbable steps increases the likelihood that we would evolve just before time runs out (favorable conditions end) becomes very high – this is quantified in the two references above.
The point which I have (still) not seen discussed much is that biologists need not be so defensive about improbable steps in evolution. I sense an almost refexive – i.e., prior-driven – response to any claims of improbability. (On the other hand, perhaps biologists just know more about the details: the claim would be that the historical record does not resemble a typical one that would be generated by a chain of improbable events. I think this question requires further study.) But the main takeaway from this analysis is that improbability does not imply design or intervention.