The effects of General Relativity only become important in extreme conditions of large mass and high densities. Our solar system does not have masses where these effects are important, but the effects of General Relativity are important in binary pulsars, since they show the necessary conditions. This letter studies the effects of General Relativity in five binary pulsar systems, and confirms predictions of the theory to a higher level than has been done in the past, helping astronomers better understand these dynamical systems.