I thought I'd post an update with my experience trying this 5K promotion.
I signed up a few weeks ago, using the EXEC5000 code to see if it would work. Nothing was mailed out, so I eventually called, and they directed me to the store to get the membership card and certificate for the miles.
The store had no problem producing the membership card, but said that the promo certs for 5000 miles are mailed out by the head office.
So I called back Costco customer service again, and got a helpful agent, who got her supervisor to look into my file and call me back to verify if the cerfiticate for miles would be processed.
In the end, they said that because I have had a Costco membership before, that I was not elegible. Mine had expired about a year ago. They didn't seem concerned that I had not personally received the mailer. So, no problem, and nothing lost. I just asked that he refund my money, which he did right away.
So, I don't think you need to be specifically targeted for this, but if you've had a Costco membership within the last 10 years, you will be in the system, and therefore won't be considered a new signup.