The 5700XT emits 0db. It’s silicon. The cooler that’s MSI used for that particular card emits 39-43dB.
What matters here isn’t noise level - that’s entirely dependent on the cooler and fan used. What does matter is TDP, as that will dictate the requirements for the cooler and fan.
5700XT by itself is a 225W part. You still need to power and cool some CPU cores (another 30-40W probably), RAM, storage, and other auxiliaries.
It can be made quiet, or even silent. But it probably won’t fit in most entertainment centers if it’s built that way at what would end up being nearly 300W.
I'm wondering about the cooler and fan and open to speculation. And companies like Gigabyte have mini GTX 670s, 970s, and so on but there are drawbacks. I had a single-fan 970 Gigabyte mini from Craigslist and it wasn't crashing or terribly slow but I sold it and got the MSI GeForce GTX 970 GAMING 4G with the red color scheme and it was much quieter and cooler.