Only upgrading the CPU from I5 6400 to I7 6700, while keeping the RX480.
To vast majority of games, almost to no fps increase.
To very few games, up to 30% more fps.
Going to i7 6700 from I5 6400 is not very cost effective, it is better to get more powerful GPU instead e.g. GTX1080 or GTX1070.
The very most effective is however to go for the new coming GPUs in 2017 e.g. perhaps Vega, perhaps GTX1080Ti.