@Phillip S. if you can’t afford to walk away from a deposit, make sure you include an inspection contingency. Also, $5k is a huge deposit; what is the price of the properties you’re looking at?
Also, as others here have said, this is just one of the difficulties of getting in the game. Honestly, if you are expecting a contractor to come out and give you a bid before you’ve even made an offer, you need to be paying for their time. Contractors are busy. Many contractors won’t even want to come out until you own the house outright, so start networking now to find someone willing to come give you an estimate while you’re under contract. Also, it could help to tell them you’re not looking for a full quote (that takes a TON of their time), but are just looking for an estimate on the work needed.
Also network with other local investors. In my experience, many RE investors really love what they do, and unlike contractors, ARE willing to donate their time (well, in my case, I’ll work for a quality cup of coffee) to help out newbies. My husband and I have walked properties with many a new investor to help them with rehab cost estimates, and also refer our contractor contacts that we’ve developed.
In short, find a way to make it happen.