Sounds like a nice tank. I am just getting into saltwater myself. Just fish so as far as I know just have to check for ammonia ,nitrites, and nitrates just like fresh water. With corals I believe you have to check levels of calcium, phosphates and some others but not sure. What size tank do you have?
How long you had tank set up for? Not trying be rude but if you don't no what test for and it's new tank your corals might die as dont like change in water quality, and most info out there says wait 6-8 months before adding corals so that gets established
Best of doing own research on net as guys in shop will just try sell you things don't need. Why think you have corals in new tank. For corals test calcium,magnesium,alkalinity,ph aswell as what you said you test above. I wouldn't risk putting corals in 5 wk old tank as water still getting stable.