Confused about test readings

[Rosebud]

I have a new 5 gallon tank. I started cycling it using the "shrimp" method on July 7th. I checked the water periodically with an API Master Test Kit. When the ammonia was at 0, the nitrites were at .25, and the nitrates were at 5.0, I took out the shrimp. I did a complete water change, just to be safe, before putting my Betta in it.

Instead, the water readings were ammonia 0, nitrites 1.0 and nitrates between 10 and 20. So, I did another full water change. Today I'm seeing ammonia at 0, nitrites between 2 and 5, and nitrates at 20.

I never have put Rosebud in the new tank. I just can't figure out how I have nitrites and nitrates and what to do about them. I thought they'd go away with a good water change, but they're getting worse instead.

Relevant info is
What size is your tank? 5 gallon
What temperature is your tank? 80
Does your tank have a filter? Yes, I believe it is a Tetra Whisper w/Bio-wheel
Does your tank have an air stone or other type of aeration? No
Is your tank heated? No
What tank mates does your betta fish live with? No fish in it now, will be only one.
What type of additives do you add to the water when you perform a water change? TopFin Water Conditioner

When I've done the water changes, I've done as close to 100% as I can. I did not vacuum or disturb the aquarium rock substrate, or the silk plants or decorative piece in the tank, as I read that I shouldn't.

I've also not done anything with the filter, other than shut it off when I did the water change (about 10 minutes). Should I do something to clean it, or is it something else that should be left alone?

I just don't get it. Any ideas? I'd love to get Rosebud out of his 1 gal tank, but am afraid to yet. Let me know if you need any additional info, and thanks in advance for your help!!

[Hallyx]

Your cycle is not finished.

The ammonia-eating bacteria (Nitrosomonas) has converted it to nitrite, but the nitrite-eating bacteria (Nitrospira) has not finished it’s job.

You have not harmed the cycle by changing water, just maybe slowed it down a little.

Running an airstone and heating the tank (>85*) will speed up the cycle. Use water conditioner. Don’t change the water until ammonia is 0.0ppm, nitrite is 0.0ppm and nitrates are high 20/40ppm. Don't clean the filter or anything else. Then do a large water change to bring the nitrate below ~10ppm and you're done.

I would put the shrimp back in and finish the job. You’re almost there.

[Rosebud]

The shrimp are history. Should I get more shrimp (since that's what I used to start with), or can I use ammonia this time? The shrimp were getting really foul and shedding stringy pieces into the tank. Blech!

How much ammonia should I use (if I can use it)?

Thanks

[Hallyx]

Ammonia is best. I never suggest shrimp or fishfood as an ammonia source because of the smell and those stringy white things. That's mold, and it's not good for your fish. Clean it out as much as feasible without scrubbing anything.

You can get "pure" ammonia at Ace Hardware or online. Shake the bottle. If it foams, it is NOT pure ammonia; don't use it.

Put a few drops in a gallon of water and see how many ppm that gets you. Ace ammonia gets me around 1ppm/drop/gallon.

Dose ammonia up to ~4ppm keep it there until your cycle is complete, when your ammonia and nitrites both are 0.0ppm.

Water change the nitrates <10ppm and you're done.