Your nitrItes will go away when your tank is cycled, or you've done enough water changes to dilute them to an unmeasurable amount. Again... you NEED nitrites for the cycle to finish out. Don't forget your goal at this point... to get your tank cycled.
Regarding my comment about nitrates, while there are mechanisms that can reduce nitrates (macroalgae, deep sand beds, etc), if you're literally pouring them back in at every water change you're not going to get much below the source water you start with. For reef tanks, the goal is to have as low of nitrates as possible. I think the commonly used "limit" for reef tanks is 10ppm or so, but in reality it's "as close to 0.0 as possible". For fish only, 5ppm is no issue at all. Just for reference, US Federal requirements for treated drinking water allow for no more than 10.0 ppm
nitrates. Normally treated drinking water from the tap will have less than 1.0ppm of nitrates.
All I'm saying is that just because it's "natural" ocean water doesn't mean it'd good, and 5ppm nitrates is far from perfect. We dump a LOT of stuff into our rivers/oceans - a lot more than our simple tests can detect.