The 5.56×45mm NATO is one of the most common rifle cartridges in the world, being the standard cartridge for all NATO countries, and also many non-NATO countries. It was developed for the the first M16-rifles during the Vietnam war. It is lighter than the 7.62×51mm NATO cartridge of the M14. This fact was very noticeable as soldiers could carry twice the amount of ammunition. During the 1970s it was chosen as NATO's standard cartridge. 5.56x45mm cartridges that propel the bullet at higher enough velocity will cause it to fragment inside of the target; lower velocity 5.56x45mm cartridges will caused the round to yaw on impact, with both methods producing lethal wounds greatly disproportionate to the bullet's relatively small size.
Being standard cartridge for military use all across the globe it should not be to hard to find in the post-apocalyptic zombie world. It is lighter than many other cartridges, like the russian 7.62x39mm or the 7.62×51mm NATO, so a survivor can carry more ammo, or just travel lighter.
Being the standard cartridge of NATO it is used on wide variety of guns, mostly rifles but also on LMGs such as the M249. Of NATO weapons can be named the M16 and M4 carbines, the FN SCAR-L, and bullpup rifles like FAMAS, Steyr AUG and the British SA80 rifle series. Like said before many non-NATO countries also produce weapons for the 5.56x45mm NATO, notable are the Russian AK-101,102 and 108 rifles, the Chinese QBZ-97, QBB-97, QBZ-03 and more, the Iranian Khaybar KH2002.