Invoking evolutionary time doesn't help. Actually, it's similar to your Churchill anecdote in some respects.
Leaving aside the historicity, there are a lot of questions begged by your story, and I'm going to ask you to walk through some of them with me.
What is the intent of the story?
If it is not apocryphal, what was Churchill's intent?
How was the woman raised? What are her circumstances? I'm personally of the opinion that women should not sell themselves for any price, but I am not particularly anxious to insult a woman just because she sees a difference between a million pounds and five. And there is a difference in many contexts.
If you absolutely insist on getting laid, five pounds will get you laid in some neighborhoods, 500 pounds will get you laid in others, etc., and in some places it takes a marriage contract.
For example, clock a byte register through all it's possible values. That's fast. Now do it randomly. It will probably take a bit longer, true? But if you have a statistically random sequence generator, it will probably not take too much time. Probably, if the generator has true statistical randomness.
How many effective bits are there in a mosquito's genes?
That's that part that's similar to your anecdote. You are assuming, when you invoke random permutation as if there were no time limits and as if mutation were the same as permutation, that five is as good as a million.
With only 59 effective bits, even at a strictly linear count with one permutation a second, you exceed the expected life of the solar system.
Now, I know you're going to claim that this is not the same problem, that we are picking relatively small strings in the genetic sequence, and that the changes are neither sequential counting nor random. But you are not asserting nature mimicking us, you are asserting coincidence between the processes.
Now that you're thinking, remember that nature works in parallel, but remember also that there is a selection involved. Some of the random stuff gets suppressed before it actually goes live, so we are not talking full permutation. And we don't have docs to tell us which combinations will be suppressed. Well, we can calculate some of the suppressed stuff, but we really don't have enough evidence to be sure of the calcuations that we can do.
The assumption that all possible permutations of a gene sequence will occur eventually is not equivalent to the assumption that all possible mutations will occur, okay?
By the way, remember that nature lopped off the dinosaurs.
Are you realy okay with saying, effectively, that it ought to be okay with everyone if our genetic experiments end up lopping humans off the evolutionary tree a little early? Is a million years not too early for you? How about five years?