Sprawler
I sent in my form around christmas, but I dont know when they got it (slow post holidays etc), I probably got my 'we have recieved' letter around the 8th of Jan and my 'phone us up for test date' letter is dated the 24th Jan, so very roughly a month. I would not worry about the 5 week wait, I was surprised how quickly mine came. BA will get back to you and the fact that it has been 5 weeks just means that you probably were not binned after reading the first page of your form. Dinnae worry.
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You came in that thing! You`re braver than I thought.