I am in Georgia, and this is my first firearm purchase. I originally filled out the form and declined to provide my SSN, but after waiting a week I went back to the FFL and resubmitted the form including the SSN. That first week of waiting isn't included in the five weeks, btw.
In Georgia they follow the federal laws that allow the FFL to transfer to the buyer after 3 days, but the FFL is not required to transfer it. It is my understanding that many choose not to, including some of the big sporting goods chains.
Of course, hindsight would have said check the policy of the FFL and find one that will do the 3 day transfer, but I didn't have hindsight back in January! Hindsight might also have said to get my carry permit first, as I understand that expedites things.
There are three factors I can think of that could be causing a delay:
1. There is a person in another state roughly my age and with the same first name, middle initial and last name that is a convicted felon. I hoped providing my SSN would facilitate making the distinction between the two of us.
2. I was not born in the USA, but I my parents were US citizens so I was automatically a US citizen.
3. The government shutdown could have caused delays.
I don't see how the first two would have caused more than a day or two's delay, not sure about the third.