Once again I have to question the famine

Genesis 46:32 says, “And the men are shepherds, for their trade hath been to feed cattle; and they have brought their flocks, and their herds, and all that they have.”  If there is a famine going on would they have many cattle?  Now that isn’t even the big question.  Why would the pharaoh let these Israelites come in the middle of a famine?  Even though they stored away five percent of their crops for seven years that wouldn’t have been much to get the Egyptians through seven years of famine.  Let alone now they have to feed Jacob's huge heard.  That would tax resources the Egyptians would need.  We know Joseph was selling grain (corn) to other peoples also.  How far can you stretch five percent of your yearly crop?