It's not hard to apply, but it will be tough to get approved. Lenders generally use your middle score and if the scores your lender obtains are the same that you report, your middle score is 572. It's often stated that FHA may consider you as low as 580, but your score is only one consideration. Your income, assets, employment history and security are others.
I would encourage you to take some time to find out why your scores are low and focus on that for a while. Low scores not only make it difficult to get approved, if you are approved your rate and terms will be tougher than if you have better scores.
Some quick tips on improving your credit are to establish and live in a budget that includes savings, anticipating surprise expenses like auto repair and to pay your bills early. Next, pay down any open accounts to 1/3 or less of their limits. Maxed out accounts drive down scores. Just don't close any accounts as that will also lower your scores. Dispute any errors you find on your credit report with the reporting agency, like Experian, Transunion or Equifax. Provide proof that the information reported is wrong and request an immediate correction.
Finally, start looking for a great local lender who can help you with this. A lender I use will review credit with a client and assist them even further. The sooner you start, the sooner you can be a home owner. Best of luck.