The lender that provided you with your pre-approval, should be the best source to answer this question. They should know the tax rate for the areas you're considering, and the typical hazard insurance costs. They are also going to have the current rates for Private Mortgage Insurance, which in one form or another, is going to be required if you put less than 20% down and only have 1 mortgage.
If your lender doesn't have the info, then as Dan indicated, you need to get a good buyer's agent to help you through this.
Here's just an example. Presuming your cost of hazard insurance for the home was $600/year, and the tax rate was running about .8%, and the loan had a monthly PMI premium of $200 (yes, it could really be this much!), then you could afford a home with a final purchase price of approximately $260,000.
Note, probably all of your $5K downpayment is going to get eaten up in fees, so consider asking the seller to cover some or all of your closing costs. And ask your lender if they actually have federally backed mortgages with less than 3% down payment, they've nearly all dried up these days. 3% of $260,000 is $7,800.
The above is just an estimate, so don't rely on it for a final decision. And remember, never borrow what someone tells you you're approved for. That's how many people get into so much trouble in the first place. Establish your budget and stick to it. Then ask friends, coworkers, neighbors and people you trust for a recommendation for a good buyer's agent.