Agree with the previous poster. You are two weeks in to the slow process of trying to grow two (or maybe more but we'll stick to the current story) types of bacteria which very slowly build their biofilms all over the sponge or other biomedia of your filter. The "A-Bacs" get off to a faster start and begin processing the household ammonia into nitrite (NO2) and lowering the ammonia level from whatever you put in downward toward a zero ppm reading. Meanwhile, the NO2 they produce is available to the "N-Bacs" which get off to a much slower start but will indeed be processing a small subset of that NO2 into nitrate (NO3) and will begin reproducing and creating their own biofilms. If I remember right it takes about 3 times as many of these cells to do the same kind of processing as the A-Bacs, so it takes a lot longer to grow their colony. As mentioned, the nitrate(NO3) is not processed by the biofilter and simply builds up in the tank. Nitrate is one of many chemicals that build up over time and must ideally be kept under control by a good weekly water change habit on the part of the aquarist. Plants, if there are lots and lots of them will also use some the nitrate but water change control is still the important habit for the beginner to learn.
It sounds like your fishless cycle is showing pretty normal feedback for two weeks. The A-Bacs are now able to take the ammonia you dose and drop it down to zero ppm. Meanwhile you are acually seeing some Nitrite build-up, which is an indication that your A-Bacs are really doing a lot of processing. Since the Nitrite is building up, you also know that the N-Bacs are not yet able to process them all very fast yet (but they are processing some because you of course are also getting some nitrate build-up. You can really drop your dosing down to 2ppm or 3ppm now so that not so much nitrate will build up during the overall fishless cycle. The higher doses like 5ppm are really just kind of a good jolt at the very beginning and can be a good measuring tool for a very strong biofilter way at the end of fishless cycling. Meanwhile 3ppm can be a good dose for the middle weeks of fishless cycling (and for tanks that will not be heavily stocked initially, the 3ppm can really carry through to the end if you want.)
What you watching for now is some progress from your N-Bacs. It can be a long time before they are first able to eat through the large backlog of NO2 and finally manage to drop that to zero ppm. Then it can still take them days to do that after a redose allows the A-Bacs to create more nitrite. Eventually though, they will eat through the NO2 in 24 hours and after that you will want to begin doing a second test at your 12 hour-after-dosing mark. Gradually your N-Bacs will get closer and closer to being able to process the NO2 down to zero ppm within 12 hours after the ammonia dosing. When you get down to the 12 hours, you can start your "qualifying week." As mentioned, this is the week where you verify that both ammonia and nitrite can be lowered to zero within 12 hours by your now large and healthy two ammonia and nitrite processing colonies. After that you make the final large water change to get rid of the excess nitrate and proceed with your initial fish stocking according to your stocking plan.
~~waterdrop~~