You are asking a question to which there is no definitive answer. Everything depends on the game. If you try to play Ashes of the Singularity, then yes, that i5 is gonna freak out. If you are playing Skyrim you'll max out the gpu long before you'll even get the cpu warm.
Most games the i5 will be fine, a few games really benefit from an i7, and a few games don't need anything more than an i3. With a 1060-6 you are probably using 1080p which will get ultra in many, even some 4k DSR, and the i5 will barely break a sweat.