Frist of all the Ryzen 5 1600 have 6 Cores and 12 threads (the i5 only 4 cores and 4 threads). Current new Games like BF1, Prey, Ghost Recon Wildlands etc take advantage of more cores.
As you said TODAY the differents in gaming is not that much but in future games the ryzen beat the i5 easy. Also some games got Ryzen optimizations like Rise of the Tomb Raider.
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Ram advice: https://geizhals.de/crucial-ballistix-sport-lt-grau-dimm-kit-16gb-bls2c8g4d240fsb-a1238860.html?hloc=at&hloc=de