Hello, I'm Keith and happy to help you with your question.
Edinburgh Council should know better. The Scots Law is:
'The relevant law is contained in the Prescription and Limitation (Scotland) Act 1973. The prescriptive period for debt recovery is 5 years under s.6 and Schedule 1.'
Furthermore, if the Council has stated that the tenants are responsible for the payment of Council Tax, why are they applying to you for recompence? This looks to me like a typical local authority 'try on' and should be most vigorously defended.
It may be adviseable to consult a trusted, local solicitor in this matter.