500k income with 580 credit score

[Jacob Souers]

I have a high end single family home that rents for 3700 per month in New Orleans. I received an application from a doctor that just finished his training and will be starting a job where he makes 560k per year. His income the previous year was under 100k and his credit score is 580. His wife that works a 30k per year job has a 710 credit score. He has offered to pay the first months rent and the last two months, in addition to a one month security deposit. That is a total for four months rent. Would I be crazy to accept his offer and let him move in?