All existing PSU cables should fit the new main board (unless you're using a psu from a dell pc, in which case it will fit with nothing), however depending on the age of it may not have a CPU power cable, which are now pretty much always required. Refer to this link to learn about PSU cables.
In a similar vein (and I have had precisely this exact issue), your PSU may not have the cables for a new GPU down the line, because GPUs now consume ungodly amounts of power. If that's the case, you'll need to replace it then, don't try to use adapters beyond the ones in the GPU box.
Overall i'm not sure this is a great upgrade. You'd be upgrading from a admittedly pretty tired CPU to an ok-to-good one, but you'd be buying into a platform that is already EOL. The advantage, of course, is that you're not spending the money on RAM and older hardware is less expensive. Then, once you're done with this upgrade, you'd still be limited by the now ancient rx480, so your CPU will be running laps around it while it struggles to ouput 30 fps in modern games. The speed of the ram isn't great, but since the GPU is so slow, I don't think it'll really matter.
I'd recommend the following upgrade path:
- first, upgrade th GPU to a 6000-series AMD card. They're about the best bang for buck right now and you will be able to keep it for a while. You'll probably need to upgrade your PSU when you do this.
- then, upgrade the rest of the system to an AM5 CPU, with basic ddr5 RAM (no need to splurge on faster), which also includes a motherboard upgrade.
- finally, upgrade your storage to an nvme drive and take the opportunity to reinstall your os cleanly, because I don't think your install is much less ancient than your gear ;)
This is, unfortunately more expensive, and in the time between the GPU and CPU upgrade, you'll really feel the CPU bottleneck (you'll feel the reverse with your plan anyway). The advantages are that you're buying into a platform that already offers great upgrade paths now, and promises greater ones in the future, as opposed to spending money just to get to the top end on your current platform.
Very hot!