Please help. Should I rent my house to him?

I have a single family house in the market for 3 months. The house located in a very good location and good school district. Yesterday I got a Black man filed application for rent. He has 4 step children and wife live with him. Kids age 10-14. His credit score 560. He has late payment in last two years for mortage and HOLOC. He said he has 5 properties and tenant did not pay him rent so made him late payment for his loan. Auto loan and credit card payment is OK. His landlord wants to move back to his house so he has to move out. He paid $ 2500/month before. My house rent is $ 2850/month.Should I rent to him or not? Should I ask to check his wife credit, too? Please help me to make decision. Thank you a lot.

Following are his explanation:
I have owned 5 homes over the years and have been a landlord myself. In fact if you pull my credit you may notice some negative items that are as a resultof two of my tenants not paying their rent and putting me in a bind in this down real estate market. So I understand the importance of paying my rent on time and our current landlord,can verify that we have consistently paid our rent on time over the past two years.

I called his landlord who said he paid his rent on time for last two years and has a very good credit when he checked two years ago,