goniopora's need high quality water, I had a green for two and a half years and my water quality was pristine, the reds or browns if you like fair better but they are a very difficult coral to keep, IMO they are not for the beginner, you could return it to the store to ensure it lives, not to be argumentative but 5ppm of nitrate is not a problem really,
you have done what most of us have and that is to stock too quickly without having quality water, but again we have all done this, As for the skimmer, well there will always be opinions, IMO they are essential for marine aquaria, Probably best to stop adding any further live stock until your skills improve so you can keep these sensitve creatures alive and well, the very best of luck though, all the very best.
Mike