Failed credit check with home owner guarantor

Guarantor

I am a first time landlord and have a tenant apply to rent my house who ‘appeared’ ideal. Couple with young child, both in permanent public sector jobs £50k income / rent £650 pcm. However, both failed credit checks and have 3 low value CCJ’s between them and each have an IVA last year. They provided two referees (homeowners) and say the IVA was to rectify mistakes when younger. Baby caused financial pressure making debt repayment difficult. But both have growing secure income and want to rent next 5 years to clear IVA and build up credit rating to buy. Whilst I accept people make mistakes I am extremely anxious and ready to refuse the application worrying that old habits die hard. Am I being unreasonable, or just suitably cautious? Potential long term tenancy BUT if it went wrong it would be horribly wrong!