Your laptop has a BIOS whitelist and the Intel 5100 is not on it
I would recommend calling Lenovo and ordering an Intel wifi card with 5 Ghz from them that will work with the X220 as the option to update the BIOS with a version that eliminates the whitelist might render the laptop useless.
I found the maintenance manual for the X220 and the Centrino Wireless-N 1000 must have been the card it was made with and it is on the list in the maintenance manual, so that is why it works
See http://download.lenovo.com/ibmdl/pub/pc/pccbbs/mobiles_pdf/0a60739.pdf on page 114 and 115 it shows the wifi cards that work. The Intel 6205 and 6300 are both listed but the 6300 may require 3 antennas. I still recommend ordering from Lenovo as the whitelist might be looking for one variation of the card and one bought from ebay might still not work