Kolmogorov's K41 theory predicts that turbulent solutions of the incompressible 3D Euler and Navier-Stokes equations possess 1/3 of a derivative in L^p for all p.  The case p=3 is known as the 4/5 law and has been verified numerically and experimentally to a great degree.  However, the phenomenon of intermittency induces deviations from K41's predictions in the case p=2, known as the 5/3 law.  In this talk, I will discuss joint work with Vlad Vicol in which we construct intermittent solutions of 3D Euler which are simultaneously consistent with the 4/5 law but not the 5/3 law.  Our work provides as well a proof of the flexible side of the Onsager conjecture which is independent from that of Isett.  The construction follows an intermittent convex integration scheme which builds on previous joint work with Tristan Buckmaster, Nader Masmoudi, and Vlad Vicol.