Life insurance coverage and the policies that you enter into offer premiums that can cover you and your family for a long period of time. When looking specifically at cancellations and refunds, the key point to keep in mind when thinking about life insurance is that you are paying for coverage throughout the term of the policy. You are generally not entitled a refund for all or even a portion of the premium payments that you have made after the term has concluded.
In your specific case, essentially you have paid for five years of insurance coverage and that service was rendered to you in full throughout the term of the policy regardless of whether or not a claim was filed. Insurance is a coverage service that is provided and paid for even when there are no payouts during the policy term. As a result, in order for you to receive a refund you would need to prove that insurance coverage during that period was not provided to you which would occur when you were not assigned a customer number or allowed to enjoy any of AARP's promised services as stipulated in the agreed upon contract. This is generally not the case with a company as reputable and experienced as AARP so this may be a fruitless exercise for you.
The only glimmer of hope would be if you canceled during a policy term that you prepaid for a number of years after you canceled the policy explicitly. In that case you are generally entitled for a refund for the months that have not yet been fulfilled from a service perspective. However, policies often have early cancellation penalties which can be exorbitant and tough to negotiate out of in the event of cancellation so that is another point to take into consideration.