Nitrates are certainly an issues in this hobby and one that is difficult to solve. Sounds like you have the nitrogen cycle under control as the ammonia is being converted to nitrites by the nitrifying bacteria and the nitrites are then being converted to nitrates. This is all a good thing since nitrates are much less harmful to marine life then either ammonia or nitrites. When I looked at your tank it appeared that there was not any growth of coraline algae on the rocks which lead me to think that the live rock may have been rock that was base rock or dried out live rock, if this was the case then there may have been an accumulation of dust on the rock and this needs to decompose just like food. Also am wondering if there is a protein skimmer on the tank, a protein skimmer can help reduce nitrates by removing some of the organics from the water that will also decompose. I also noticed that you have a shallow sand bed in the tank, my thinking and certainly not an expert but you should either go with a deep bed or no sand as a shallow bed does not allow for the anaerobic bacteria to grow in the tank which is benificial in the removal of nitrates as well. Suggestions: (1) install a protein skimmer or get a larger skimmer, (2) purchase a few good pieces of live rock that have coraline growth on them to seed your tank, (3) feed the fish a bit less to get the nitrates under control. and (4) do small water changes daily say one or two gallons to refresh the water daily until you start to see nitrates go down. I think if you do these things you will see that your nitrate problems may decrease to around the 5 ppm's or less.