Tenant screening - need help

[Flora Granter]

We got a tenant application for a 2006 single family house with monthly rent $1425. The applicant has a nice credit score of 702 and monthly income of $5000. Based on tenantsearch check, he has no criminal history and no eviction history. But he is from CA with two recent short-term contract job ( 4-month, 12-month) in Houston. He has two large debt:one $22k for vehicle; the other $20k. He has a credit card debt over $6000. He has two large dogs: 20 lbs French bulldog and 60 lbs pointer. He has a co-applicant who is his finances. She actually lives in California and they have a house there. She has 788 credit score and only has a house payment with monthly mortgage $1400. She has decent income $8000 monthly. I requested his bank statement and was told he is not comfortable with that. But he is willing to show his paystub. I requested increased non-refundable pet deposit due to the pet size from standard $250 to $400. He was not interested in the increased amount. My rental house has been vacant since end of November. I hope to rent to this tenant. But kinda of worries of his debt and his job stability and potential house damage from his large dogs. Please help me whether I should rent to this tenant. Your advice is appreciated. Newbie me wants to know comments and experience.