Stop Illegal Reentry Act or Kate's Law This bill amends the Immigration and Nationality Act to increase from two years to five years the maximum prison term for an alien who re-enters after being excluded, denied admission, deported, or removed. The bill establishes: a 10-year maximum prison term for an alien who re-enters after being denied admission, excluded, deported, or removed on three or more prior occasions; and a 5-year mandatory minimum prison term for an alien who re-enters after being removed following a conviction for an aggravated felony or following two or more prior convictions for illegal re-entry.