In this study, we obtained the characteristics of possible collisions with the Earth for a number of dangerous asteroids: 443104 (2013 XK22), 2015 RN35, 2008 EX5. Most of these impacts were previously unknown. Possible approaches of asteroids to the Earth, and previously obtained possible collisions with the Earth of the asteroid Apophis are also discussed. The results obtained indicate that the number of possible collisions with the Earth of dangerous asteroids is significantly greater than was previously known. A thorough study of these collisions, as well as of the preceding approaches with the Earth, is an urgent task.