Am I obligated to repay a sum that an elderly woman claims her husband, who passed away five years ago, lent to me, despite my full knowledge that this did not happen and that she did not inform me of this throughout this entire period?

What the woman said is a claim. If you do not know the truth of it, then she must present legitimate evidence to prove the validity of her claim; otherwise, it holds no value. If she has no evidence and takes the case to a judge, you will be asked to take an oath to deny this claim. The legal principle in this matter is that "the burden of proof is on the claimant, and the oath is on the defendant," based on the Prophet Muhammad's (peace be upon him) saying: "Were people to be given according to their claims, men would claim the blood and property of others, but the burden of proof is on the claimant, and the oath is on the defendant."