Should I upgrade my AM4 system or switch to AM5 with a €300–€500 budget?

With roughly €300, staying on AM4 is the sensible option. Even if selling your current parts gives you around €500 total, a complete AM5 upgrade still requires a CPU, motherboard, and DDR5 memory, so you would likely end up with a lower-end setup that isn’t clearly faster. A Ryzen 7 5700X or one of the cheaper X3D chips could be a better-value upgrade, and adding another 16GB of DDR4 would bring you to 32GB.

I’d stay on AM4 for now. Moving to AM5 only makes sense if you can afford a decent motherboard, processor, and DDR5 kit without compromising too much. Your current platform still has useful upgrade options, and 32GB of memory is increasingly worthwhile for modern games. You can save for a larger AM5 upgrade later instead of forcing one into a €500 budget.

The 5800X3D would be a substantial jump from the Ryzen 5 3600, especially in CPU-heavy games. However, check prices before buying because the 5700X3D or 5500X3D may offer much better value. If your games are mostly GPU-limited, a Ryzen 5 5600 or 5600X plus 32GB of RAM may be enough and would leave money for another component.

There is one argument for AM5: it gives you a longer upgrade path, while AM4 is effectively at the end of its lifecycle. But at this budget, the initial AM5 system probably won’t outperform a good AM4 upgrade. I’d compare local prices for a 5700X3D, 5500X3D, or 5800X3D, and only switch platforms if you find unusually good deals on used parts.