I've heard of the "silent cycle" that can go on in planted tanks, but I never assumed mine would qualify.

(I know the image isn't showing up, not sure how to fix it. If you right click and open it in a new tab it can be viewed, or at least that's what worked for me).
I have a six gallon pillar with some banana lillies, anacharis, wisteria, and water sprite. Is this enough to start a silent cycle? The tank is suppored by natural light and receives no ferilizers.
I first noticed something was off when I tested my water before my weekly water change and got a reading of 0 ammonia. So I decided to go on and test my nitrate and nitrate. Readings as follows:
- Ammonia: 0 ppm
- Nitrite: 50 - 1.0 ppm
- Nitrate 5.0 - 10 ppm
I'm assuming a water change is due to knock down my nitrites at the least, but I did a test on my tapwater as well and it comes up as 1.0 ppm without treatment. After some research I bought prime to detoxify that, but when I did a test of the treated and untreated water they both came up as 1.0 ppm. Would prime treated water, while showing 1.0 ppm, be less toxic?
I got the 6 gallon without a filter because I didn't want to deal with a cycle, but as long as there's one going on I'd like to know how to support it so it will finish out.
The question here is what is worse? High nitratites that are being converted into nitrates or doing a water change with water that is fairly high in ammonia?