If you have fish do NOT dose ammonia. I would not consider it unusual for the Nitrites to disappear. Thats the purpose of cycling. The ammonia is changed to Nitrites by bacteria. It takes some time for that bacteria to develop. A different strain of bacteria convert the Nitrites to Nitrates. That bacteria starts to grow when the Nitrates are created. (Thats why it takes so long to cycle a tank) If you did a water change prior to testing that is probably why your Nitrate level is low and at 5 I wouldnt be worried about it all that much. Keep it at less than 10 for sure. A partial change will lower it or if you plan to add plants that will help keep the Nitrates down.
I know it's hard to look at a box of water but let me add this, and this is something I am still cultivating as I am building my first saltwater tank. Patience is everything. Dont rush to stock the tank until you are 120% positive the tank has fully cycled. Add stock gradually, not all at once, so the bacteria will adjust gradually to the increased bio load. As David Carradine often heard, "Patience, Grasshopper."