Sorry but I did understand your question, I guess my answer was less than detailed.
After a proper cycle you should have more that just 5 ppm
nitrate. That means you didn't cycle enough ammonia to build a strong enough BB colony.
Adding only a small cuc should not cause a mini cycle. Another sign you don't have enough BB.
Now I think you have 2 options. Remove the cuc to a QT and recycle the tank with a larger ammonia source so you increase the colonies of BB that are starting to establish themselves. It should be quicker as the 2 types if BB are already present.
Or if your amm go down to 0 right away, you could consider adding 1 fish and keeping a close eye on amm again. Slowly building up the population. But if the amm starts to go up you might need to QT it and do the first option anyhow. Your choice. Good luck