It's extremely unlikely that he could win on that. The law in Georgia is that when a parent voluntarily gives up parental rights in connection with an adoption the parent has four days to revoke that consent. See Georgia Code section 19-8-9. But when the parent gives up parental rights not connected with an adoption, the Georgia courts have held the statute does not allow any time to revoke the consent to termination of his/her parental right. Thus, in the case of a mother who gave up parental rights where there was no adoption and then sought to revoke her consent just a month later, the Georgia Court of Appeals said that was not possible:
Moreover, even if the mother's argument had been properly raised, it would still be without merit. There is no grace period written into OCGA § 15–11–94(b)(1) that would allow a parent to voluntarily consent to the termination of his or her parental rights, and then withdraw such voluntary consent over one month later. See id. Nor is this Court authorized to invent statutory language that would authorize such a grace period where none exists in the statute as written. See U.S. Life Credit Corp. v. Johnson, 161 Ga.App. 864, 865(1), 290 S.E.2d 280 (1982) (“This court cannot add language to a statute by judicial decree.”) (citation omitted). If the legislature intended for a grace period to exist in the statute, it could have expressly provided one. See, e.g., OCGA § 19–8–9(b) (expressly allowing ten-day grace period to withdraw consent to surrender of parental rights in adoption proceedings).
In re T.C.D., 281 Ga. App. 517, 518, 636 S.E.2d 704, 705 (2006). The statute section the court cited, § 15-11-94, has been amended and renumbered since then to § 15-11-310. Despite those changes, it appears to still be the case that GA law allows no time for the parent to revoke his consent for termination of his parental rights, and certainly not five years. That being the case, he'd likely have to prove the consent he gave was not voluntary, e.g. there was fraud, duress, or that he was incompetent at the time. Even then, the fact that he waited so long will work against him.
If he brings an action to reinstate his parental rights, see a GA family law attorney for assistance with that. Even though it may be very unlikely that he could win, you still need to properly respond to the lawsuit to ensure the best outcome.