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If you've been using a Core i5-2500 for the past 8 years, then you have gotten plenty of value out of that CPU and motherboard. It would be easy for us to suggest spending more of your money on more cores to get a US$329 Ryzen 7 3700X (8 cores, 16 threads) rather than a US$198 Ryzen 5 3600 (6 cores, 12 threads). The additional cores would likely allow the CPU to keep up with future software demands for a longer period, but you probably know your needs better than we do. Back in January 2011, the top desktop CPUs had 4 cores and SMT. You got one with 4 cores and no hyperthreading. In September 2019, the top desktop CPUs have 8, 12 or soon-to-be 16 cores and SMT. The 8-core Ryzen 7 3700X is further from the top than your Core i5-2500 was in its time.
The CPU coolers included in the box with the AMD processors are generally well-reviewed by folks that don't overclock their CPUs.
1: i7-9700K, NH-D15, Z390M Pro4, 32GiB, RX Vega64, ½TB 960Pro +2TB MX500, Define Mini-C, SSR-850PX, LG 32UD99 + UltraSharp U2410, RK9000V2-BR
2: R5-3600X, Wraith Spire, B450M Steel Legend, 32GiB, RX5500XT, 2TB SX8200Pro, P160, SS-660XP2, TV, G610