<puts on serious hat>
it stands for 'And I Claim My Five Pounds' relating to people posting a QOTW answer and people guessing who they were referring to 'claim £5'. I would put an exmaple below but would only humiliate myself with a lack of ability to write a suitable bit
(Studentken is looking for motivation on, Fri 9 Dec 2011, 8:46, 2 replies)

I believe it actually relates
to a competition, details of which escape me.

Let's imagine it was run by a radio station, or something like that. They would send an employee out each day, and the audience would have some way to track down this employee. When they did, they would win £5.

They would be required to say 'You're [whoever], and I claim my £5'. Said employee would then hand over the crisp fiver.

Edit - it's explained properly on the link above. It was a newspaper.
(username failed moderation, Fri 9 Dec 2011, 9:42, closed)

This was a common phrase a LOOOOONNNNG time ago - like maybe the 1960s?
It probably only survives as a concept here in B3ta - the graveyard of memes.
(moon monkey is busy making memories worth repressing, Fri 9 Dec 2011, 10:40, closed)

Also plays a part in Brighton Rock
Kolly Kibber or something? You went up to him and said "Your Kolly Kibber and I claim my five pounds"
(Che Grimsdale Best before:, Fri 9 Dec 2011, 10:46, closed)

Viz
It was also run a lot in the Viz letters page, where the variation would be someone writing in and ending the letter (for whatever reason) with 'Do I win £5?'. Sort of like 'length?'..
( DeadEyeDick, Fri 9 Dec 2011, 11:30, closed)