What is the ruling of the Shari'ah and the law regarding a wife who requests divorce under duress, then flees to another country and is absent for five months, and what should the husband do who refuses to divorce her?

You are not obliged to divorce your wife. By abandoning the marital home and traveling without your permission, she is considered rebellious (nashiz), unless she has a legitimate excuse according to Islamic law. A rebellious wife is sinful and disobedient, and she is not entitled to maintenance (nafaqah). To learn how to deal with a rebellious wife according to Islamic law, please refer to Fatwa no. 33210. As for legal procedures, you should consult with specialists.