@Caden Glenn sounds like you need to find a great Realtor to talk to in your area! I'm not in Cincinnati, but these are all things I cover in my buyer consultations.
1. You can do as little as 3% down as a first time homebuyer with a conventional loan, assuming you qualify. You can also do 0% down if you want to go the USDA or VA route, or perhaps could qualify for down payment assistance. Depends on your situation and what local options are available in OH.
2. Closing costs should be closer to the 3% than the 5%. If you were paying 5% closing costs on a $300k purchase price, I'd tell you to find a different lender.
3. Inspections vary, and depends on what you want. In NC (no idea if it's different in OH), a standard mechanical inspection depends on the size of the property, if it's a crawl space, slab or basement foundation, etc. Typically they run $500-$1000 depending on those factors and any additional inspections your Realtor recommends.
4. Appraisals are another item the lender may require to be paid prior to closing. In the CLT area, it's usually $500-$700.
If you're gearing up to buy a home, especially since it's your first time, talk to a Realtor who can prepare you for these expenses, what to expect as far as deposits, as well as connect you with a fantastic lender who will be able to advise/guide on the lending side.
Best of luck!