5.56 from the sheriff:
In Megaton (the nearest town from the asylum), you can get an automatic 5.56 almost gift. In Salun, Mariardy sits Mr. Berk. He will offer to blow up a bomb. I will advise to abandon the explosion and report this sheriff local. Sheriff will run to arrest Berk. And when he behaves in Turm, Berk will shoot him in the back, and you mind it (preferably through step-by-step mode). From the sheriff body take 5,56 automatic.