no, it will not bottleneck given especially two extra cores and higher clock speed than 8400. Gaming at higher resolution WQHD and above is typically more GPU bound than CPU and assuming that's your target resolution. Also high refresh rate is also not bottle-necked by current gen i5.
But i would suggest 9400F if saving few bucks helps and its kind of an 8500 only with its clockbumps given without the iGpu, or ponying up for 9600k given its priced too close to an 8500/8600 non k.