The banding looks like 8 bit quantization noise to me since it looks very much like synthetically generated images where I have seen the same thing and know that was what was going on. Generally 8 bits per color per pixel is good enough, but not always. With a slowly changing flat area with little noise you can see banding with 8 bits, which this certainly looks like.

No, this is not likely the fault of your camera. I didn't look up what the width of raw values from a Nikon D5100 are, but very likely more than 8 bits. Assuming you were using near the full dynamic range of the sensor, the raw image won't have this level of banding. The problem is that just about all display systems use 8 bits per color per pixel, so therefore any post processed image will be limited to that. Even with a higher depth post processed image, you'll still be back to 8 bits/color/pixel on most displays.

It may sound like you're screwed by the physics, but there is a way to fix this. The solution is dithering. A simple 2x2 dither pattern gives you effectively 10 bits/color/pixel, which is enough to make the banding dissappear. Dithering a 8 bit intensity with a fixed 2x2 pattern will be invisible for practicle purposes. Even if someone is pixel peeping, it will be very difficult to notice the change of 1 value between adjacent pixels. The funny thing about dithering is that it works better the less you need it.

There is one gotcha though. While dithering from the raw to the final 8 bit image will eliminate the bands for practical purposes, it will cause trouble with some compression schemes. JPG compression may decide that the adjacent values are close enough and "skip over" the dithering. Other schemes may not compress well. LZW compression as is common in TIF files will work well. If the end result is a JPG, select the highest possible "quality" level (usually 100) and check whether it flattened the dithering or not. You may have to stick to lossless compression schemes.