Help with new tank (new to me)

I need some insight. Let me start from the beginning.

I bought a 75 gallon tank with live rock and live sand. The previous owner drained the tank a few days before i picked it up. She layed the rock down i the sand to help keep them wet. When I picked up the tank the sand was still wet.

I got the tank home, spread the sand out and filled the tank with ro/di water and added the salt and added a dead shrimp to cycle.

I started testing the water 24 hrs later

First test ammonia was 1 ppm, nitrite .5 ppm and nitrate 160 ppm

Next day ammonia was 2 ppm, nitrites were at 1 ppm and nitrates were at 160 ppm

Third day same numbers except nitrites were at 2 ppm

Fourth day ammonia was at 1 ppm, nitrites 5 ppm and nitrates at 160.

Sixth day through today (12th day) nitrates still at 160, ammonia and nitrites at 0. On 6th day i took the shrimp out.

On 7th day I added two clownfish because the lfs said to let the tank finish cycling with fish.

My question is, will the nitrates drop on their own or do i need to do a water change now?