Can personal checks that were given as gifts 5 years ago and never cashed be presented for payment at the time the estate is settled?

No. First of all, those checks likely would not be honored by the bank anyhow. Second, the account should be frozen after the death of the owner, so the checks won't clear. At best, the holders of the uncashed gift checks can try to claim the status of unsecured creditors of the estate, and try to have the estate give them new checks. Which raises the question for me: why weren't the checks cashed in the first place?