It has been 5 working days and I have not received my SIM card yet.

[ragoneld]

What can I do?

[bristolian · Accepted solution]

Replacement SIMs are sent out by Royal Mail second-class post.

If you are near an EE retail store, they can issue replacement SIMs face-to-face with photographic ID.

This assumes it is a replacement SIM you're waiting for.