I was originally going to post this as a comment into the UFAI & great filter thread, but since I noticed that my comment didn't include a single word of AIs I thought about making an entire new discussion thread and I continued writing to improve the quality from comment to post. The essay is intended as thought-provoking and I don't have the required knowledge in the related fields and I mostly pieced this together by browsing wikipedia, but hopefully it gets you thinking!
Personally I think when considering the Drake Equation it's important to note that it actually took ridiculously long for intelligent life to evolve here and that we're on a finite timeline. The drake equation contains the rate of star formation, the number of planets in the stars, it even has a variable for the time it takes for life to evolve to the point of signaling detectably into outer space, etc. but it's also important to pay attention to that the average setup of the universe has changed.
On earth life has existed for almost 4 billion years and it has only been 43 years since our civilization first visited the moon and ~1½ centuries since the invention of radio? That is a very small time frame. Particularly if we consider that ~4 billion years is between a quarter and a third of the age of the universe itself.
When we consider the Great Filter we can at least propose that there have been several mass extinction events which failed to end all life on earth. I think it's a valid argument to say that for an example any powerful impact could have ended all life or reset the evolution of life some/any number of degrees - and it has been ~70 years since the initiation of the Manhattan project and already humanity has the potential to go through a thermonuclear war that could end human life on the planet, or rollback the game of life through nuclear winter. Mars could have been habitable. For an example there's no liquid water on Mars now, though there should've been earlier. The habitable zone as theoretized is considerably narrow - For an example: If at any point in the history of (life on) earth the average surface temperature had climbed to 200 celsius for whatever reason I'm pretty sure that would've made our planet like all the other planets observed - so far - in that they don't seem contain intelligent life. What I mean by this is that even though a vast number of planets reside in the habitable zone of some star, they have to maintain those conditions for a very long time, and that's just one variable. Which by the way is a pretty important thing to note when talking about things such as the greenhouse effect for an example. Some people seem to have this idea of "natural balance" that occurs automatically. It's as if those people are not looking at the "natural balance" on some of the other planets. Where's the mechanism anyway? Milankovitch cycles? Even algae managed to start an ice age according to some theories, humans certainly have the potential to do more harm than that and it's not like we only have to care for extinction events that we brought upon ourselves.
In addition to this it seems to me frequently neglected that the conditions inside the universe have changed considerably with the aging universe. Earth is not constantly bombarded by collisions, it takes time for stars and planets and so forth to attain their form, the average age of stars has changed. In other words the habitability of the entire universe changes over time, though not in a particularly synchronous fashion. If this does not seem reasonable then consider the following: Was the likelihood for finding intelligent life in any location of the universe when it was 1 billion years old the same as it is today? How about when the universe was 4 billion years old? 8 billion years? Most stars are between 1 to 10 billion years of age according to wikipedia.
Human species itself has gone through some sort of a bottleneck, a historical token worth reflecting upon: Had the event been worse and those few remaining members of our ancenstry perished the planet earth would arguably still be without intelligent civilizations even today.
This line of reasoning in my opinion favors two different details:
1. Since our intelligence took almost 4 billion years to evolve, any event within that time that could've wiped out all the progress, would've occured before the rise of intelligent civilizations - and so all those events contribute to the Great Filter
2. The often contemplated likelihood that human intelligence is among the earliest intelligent species to arise, if life had been considerably less likely in the earlier stages of the universe. (which is very complatible with the fact that we have not observed life elsewhere - or at least that's somewhat complementary to likelihood of intelligent life) In otherwords if our species is within the first 5% of the intelligent civilizations to arise that should be reflected upon our observations. Of course the same is true for the last 5%, etc. This is an important point, because that's not the kind of reliability science rests upon.
Remember how life taking almost ~4 billion years to evolve on earth was a ~1/3 (rather ~2/7) of the age of the entire universe? Well our solar system is only 4.6 billion years old. Life on earth has been evolving practically since the formation of our solar system and at no point in time were all the replicators wiped out.
So, any thoughts?
I think the Drake equation isn't really the way to estimate the probably of intelligent life - there is just too much we don't know to use the inside view. Take one thing like the Moon and we just don't know how important it was to have intelligent life on Earth (it definitely played a significant role, stabilizing the Earth orbit, and helping the sea => land transition with tidal forces) nor how rare such big satellites are.
To me the only way to look at it is to use the outside view, and do a reasoning like :
Look at us, and, like you said and realize it took us 5 billions of years to exist, which is actually half of the lifespan of Earth. We don't know if we were exceptionally fast or exceptionally slow, but it gives an order of magnitude of the time it takes for intelligent life to appear on a planet with good conditions.
Realize that it would be exceptional coincidence if another intelligent life would appear within 0.1% of the time it took us - so if there is intelligent life somewhere else, it's likely to be 5 millions of years in advance, or 5 millions of years late from us. 5 millions of years late means they are still apes.
Look around us, and see no trace of alien life - no Von Neumann probe visiting our system, no Dyson spheres or ringworlds around. And yet, if they were 5 millions of years in advance, we would very likely see such things.
So either there is a "great filter" and most of them didn't make it to space, or just, well, intelligent life is rare, because it takes in average 20 billions of years to appear even if conditions are good, and we were lucky to be fast enough to exist before the Sun became a red giant. Which that there will be occasional intelligent life in the universe, but so far apart that we didn't see them yet. If our nearest neighbor exists since 0.3 billion of years, but is 0.5 billions of light year from us, well, we'll sill need a long time before communicating with them.