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Cory cats aren't well suited to an uncycled tank. Oto cats are especially bad. Honestly, I wouldn't expect the Oto to survive in a new tank and without a good algae supply. Is there anyone you know who has an established tank that could take him?
I would advise to have liquid tests for Nitrite and Nitrate, as well. The test stripes are notoriously inaccurate. The API Master Kit is what most of us here use, and is accurate when performed correctly. (Though, the instruction advise shaking the #2 Nitrate bottle and the test tube for much shorter than necessary. I would shake both for 2 minutes. And I mean really
shake them! I beat mine against a table.)
You'll want to have both of those test kits so you can both watch your cycle progress, and so you'll know when to do 50% water changes (i.e. when you have Ammonia or Nitrite readings above 0ppm, or Nitrate readings above 20ppm, or weekly, whichever comes first). You can pretty much expect to do a water change at least once a day for 6 to 8 weeks while the cycle runs its course.
Five small Cory cats is a pretty hefty load on an uncycled 10g tank. I would expect the Ammonia, etc to spike early and pretty high. I would start doing 50% water changes daily while you're waiting to purchase the tests.
There are two other very helpful things you could do. The first is to get lots of fast growing plants to help suck up the ammonia, etc. The faster the plants grow, the faster it uses the ammonia, etc before it gets a chance to harm your fish. Examples of good choices are Water Sprite, Brazillian Pennywort, Hornwort, and Duckweed. (Though, be warned that some people conisider Duckweed a pest, and its true that it can be hard to get rid of once you have it.) But before you choose your plants, we can help you look at the type of light you have and pick plants that will be appropriate. What plants (and how many of each) do you have already? How many and what type of bulbs do you have? What do the bulbs say on them? How long do you have them on each day?
Another helpful thing you can do is to borrow something from a healthy, established tank that will have beneficial bacteria on it. This is called a "seed". This will help jump start your cycle. Things such as a used filter cartridge, used bio media, or used gravel/substrate wouldl be good choices. You can either place the seed in your filter, sprinkle the seed substrate on your substrate, or place the seed in a well-rinsed (no soap) knee high or cut off pantyhose leg and set in in your tank. Sometimes a LFS will give you seeding material, but I think this is suspect. I mean, any LFS or chain goes through a lot of fish, and is therefore exposed to a lot of fish disease. Problems like Ich can be transmitted via gravel, etc. So I would be more inclined to get seed from an individual, or possibly someone from a local Aquarium Society. Or you may get lucky and find someone on here that lives near you, if you feel comfortable with saying what city you live in. I'm in Cincinnati, myself.
I know its a lot of information, but you'll get it. And in the meantime, we're here to help. TFK is a great resource, and there are a lot of very smart cookies here, and very experienced and very nice to boot! We'll help you any way we can!