Yes, the Ryzen 5 1600 is better overall than the i5 6500.
Both are 14nm lithography, rated at 65W TDP, and have 3.2GHz base clock speeds to 3.6GHz boost clock speeds (though may not be an apples-to-apples comparison due to different IPC). The Ryzen 5 1600 has more cores and threads with multi-threading (at 6 core and 12 threads) versus the i5 6500 with only 4 cores with no hyperthreading. Ryzen 5 1600 is also an unlocked CPU (i.e., overclockable when paired with a B350-chipset or X370-chipset motherboard) versus the i5 6500 which is locked/non-OCable. The Ryzen 5 1600 has a 16MB cache while the i5 6500 only has 6MB. Ryzen 5 1600 comes with a beefier stock CPU cooler while the i5 6500 comes with a mediocre one. Main advantage of...