It sounds expected but not right. You need to do partial water changes using dechlorinated water very regularily to keep those nitrites down. You sound like the ammonia eating bacteria have formed but the nitrIte eating bacteria have not. The latter takes at least twice as long to develop than the first.I have been doing a cycle with fish for 8 days and my readings are
Ammonia: 0 ppm
Nitrite: 5 ppm
does this sound right