It depends on which game are you playing, I had a GTX 1060 too and I was getting a heavy cpu bottleneck on Black Ops 4, but also on Rainbow Six Siege and on Fortnite a little. All this with an i5 6500 and playing with a 180hz monitor. I solved my problem changing my cpu to a Ryzen 7 2700X. You can check the i5 6500 specs on Intel's website, but it's very similar to yours.
Edit: I don't remember if gpu usage was dropping or still high, but I'm sure cpu usage was often or always at 100% on these games and others.