Just a Wild Thought :
Create a Customer Account ( Name it as Customer X AMC Account)
Add an Entry of Payment Recieved from the customer in that Account - So this account has Positive Balance.
Now Create a Contract / Scheduling agreement for 5 years for that Customer Account (the new one - AMC Related)
Every year the billing can be created and can be reconcilled with the balance already present in the AMC customer account.
This will allow the proper entry into your books for accounting as the payment received will not be shown as your income till it is realised every year.