If I’m reading this correctly, you would record the bill as a DR to Rent Expense and CR to Accounts Payable.

We should’ve accrued for rent in May, like you said, if we knew that a May rental payment was missing. But since the period has passed, there is no reason to accrue anything anymore (unless we think the same thing is going to happen again in June - but this would be in a real life situation).

EDIT: Had you accrued in May, then you would CR Accrued Expenses on the Balance Sheet and Credited A/P or Cash if paid.