She wants to travel for five months away from her husband

Praise be to Allah.

If the couple both agree to that then there is nothing wrong with it, unless staying apart will lead one of the couple to do something wrong such as doing something haraam or neglecting the children. In this case it is not permissible, because the Prophet (peace and blessings of Allaah be upon him) said: “There should be neither harming nor reciprocating harm.” And Allaah knows best.