Without a dBa @ distance measurement, with comparisons to other equipment using the same measuring equipment, "quite loud" is not really a useful characterization. Even then the dBa level alone doesn't tell you all you need to know about the acousic objectionability factor. My good old AOpen MP945 with GMA950 graphics (exactly the same size as the good, original Mac Mini) idles and even does useful light work in silence in a quiet residential room with nobody else in the house to make any noise, and without any radio or TV or air conditioner running. Even all out, it is plenty tame, on the good side of laptop noise. The cooling system in a dynamite design.
But my AOpen GP7A with the power hogging NVidia graphics, even sitting idle, periodically roars like a bastard as some random daemon makes a quick tiny demand. When it is really working it sounds like a freight train or jet plane taking off, and oven-like air is rushing out of it.
The NUC takes even less power than the MP945. Certainly the 5i3 is damn quiet. I expect the 5i7 isn't all that noisy. I'm pretty certain it is a damn sight quieter than that GP7A.