572 will be challenging. Many will go to 620 for the low-mid score (middle credit scores are used -- if more than one borrower is on the loan, it's the lowest middle score of the borrowers). There are price hits for lower credit scores that can be steep. Home owners insurance rates may be more too (based on credit score).
I really recommend first meeting with a mortgage originator you trust to review your credit. It could be some simple adjustments that will help pop your score up. You would be surprised at what hurts your credit--for example, if you're paying off and closing your accounts, this may actually LOWER your credit score even though this seems like the "responsible" thing to do.
I'm happy to review your credit at no obligation to you.
Most of the information below is mostly correct. The short answer is yes, you can get a loan. On FHA, which is only 3.5% down, you will need at least a 580 credit score, most lenders want at least 620. And, of course, there will be mortgage insurance. There some Homesteps homes on the market which are owned by Fannie Mai that you can buy with 5% down and no mortgage insurance. Then there is USDA rural housing loans with 0 down out in the country. ( I can let you know in detail where they are, you you can log in to their site and see for yourself. As to your credit scores, it would be good to get them up higher and keep them that way. There is a company that has been doing that for over 10 years and they are 100% successful at what they do. I can put you in touch with them if you want.
If you want to consult further, I would be happy to work with you. I am a loan officer and a real estate agent and so I can help you with all of it. Feel free to give me a call at 206-841-9976, and let's find you a home.
I don't mean to discourage you, there may be something that can be done I just don't want to see you or anyone get in over their heads with higher then normal interest rates or insurance costs. I know a few loan officers that I have personally witnessed help questionable credit, if you need a referral please feel free to contact me.
A loan originator I work with has been able to work wonders with challenging credit scores. His name is Keith Yamamoto - 206-250-9360 - email@example.com. He's very friendly and easy to work with.
Best of luck and congratulations on taking steps to get into a new home!