You are in the nitrite spike stage of fishless cycling. You just go steadily along, logging your test results in your aquarium notebook and here in your thread if you do that. One little tweek that OM and I like to try is to lower the dosing down to, say, 3ppm, during the nitrite spike stage, so that not as much overall nitrate will ultimately get produced.
You are correct. The nitrate(NO3) will indeed go higher than the 5ppm limit of the test, but that's ok, all you really care about is that you are still "in" the nitrite spike stage. Sometimes this stage seems to take forever but eventually, one day, the nitrite spike will suddenly drop off (and I mean suddenly - sometimes it drops to zero in a single day.) That will usually mean that nitrite will be processed to zero ppm within 24 hours after dosing from then on and the number of hours it will take will slowly go down.
At that point you have moved into the 3rd stage of fishless cycling and watching to see when nitrite can be cleared within 12 hours of dosing becomes basically your main goal. As you get closer to that goal you raise your dosing back up to 5ppm to maximize the size of your bacterial colonies by the end. You only ever dose once per 24 hours, even once you start testing at 12 hours to see your 12-hour results.
~~waterdrop~~