A (4,5)-coloring of Kn is an edge-coloring of Kn where every 4-clique spans at least five colors. We show that there exist (4,5)-colorings of Kn using 56n+o(n) colors. This settles a disagreement between Erdős and Gyárfás reported in their 1997 paper. Our construction uses a randomized process which we analyze using the so-called differential equation method to establish dynamic concentration. In particular, our coloring process uses random triangle removal, a process first introduced by Bollobás and Erdős, and analyzed by Bohman, Frieze and Lubetzky.