Have a read of the following two PDFs, if you haven't already, whilst they're not specifically for the NX5, they're still relevant:
http://www.sony-asia.com/microsite/professional/hdv/pdf/HVR-Z7_S270Tutorial_e7.pdf
http://www.sony.co.uk/res/attachment/file/62/1237483683462.pdf
Re you're issues, as Drew says, it's far easier to advise having seen a good example, but taking what you've said so far, I think worth breaking it down a bit. You've mentioned sharpness, grain, artefacts and colour as issues, whilst some of the issues may come from the same source, I'd suggest looking at them totally separately.
- Colour (green tinge) : looking at your picture profile, you've put in a phase of +2 (shifting to red), a colour depth of +2 on red and -2 against blue. This change will be applied after white balancing, so if for instance you held up a white sheet of paper and did a manual white balance, the resultant image would take on a red'ish green hue (because you've made a strong push on red and a weaker reduction of blue... green sits in the middle)
- Sharpness : don't compare you're footage to a GoPro, GoPro video files are massively processed with heaps of sharpness, contrast and saturation, and also work on a hyper focal distance of very close to the lens to a very long way away. I.e everything is pin sharp in focus we added sharpness added in as well. Currently your detail is set to 0, try increasing this a bit, perhaps +3, to see how it looks.
- Grain : by this, I'm assuming you mean noise? In which case, it will be created by applying gain to your image, either by the gain setting on the camera, or possibly by trying to white balance in a severely out of colour balance (e.g when white balancing at 20ft, it would need to apply a lot of gain to red to colour balance across all channels, noise could result). Solution there, try and avoid gain situations, either by adding more light (video lights), or bringing the colours more in to balance before trying white balance (red/magenta filter)
- Artefacts/blocking : Seeing an example would help, but at a guess, this is happening in the low light areas, i.e. shadows and blacks? If so, then put this down to the fact that you are recording an 8 bit signal. Somebody more intelligent than me will undoubtedly explain the ins and outs, however in simpleton terms, 8 bit recording isn't that much data space, something has to give, so some of the available space for the lowlights and shadows is robbed and given to the mid tones and highlights, as these are the areas that you are most likely going to want to see in the end image. The solution to this is to try and lift the exposure to reduce the amount of shadows/low lights.
You mention that you've also tried a few different camera settings, shutter speeds etc. Keep that simple. put the camera in 25p (or 50i if you want the interlaced look), shutter speed at 1/50th second, gain at 0db and then use purely the iris and ND filters for exposure control. I'd also avoid using auto unless your shot will switching between different light situations, throw it in manual and use your zebras and histogram to keep the exposure as light as possible (and so avoid the tricky shadows) without blowing out the highlights. My zebras are set at between 75 to 85, dependant on what I'm shooting (and who for).
Also, worth getting yourself a colour chart and doing some tests in the top side environment. I'd start with everything (in the picture profile) set to zero and then work your way from there, get the camera set to create the look you want.
