Is it permissible for a woman to seek divorce from her husband after five years of marriage due to her discovery of his continuous lying before and after marriage, his neglect of his family, his lack of concern for his daughter, in addition to his addiction to smoking and committing sins, knowing that the husband is willing to change?

If a woman dislikes her husband and fears that she will not be able to fulfill God's rights (duties towards him), then there is no blame upon her for seeking divorce, whether through khul' (divorce at the wife's instance, usually by returning the dower) or otherwise. This is supported by the Almighty's saying: "But if you fear that they will not uphold the limits of Allah, then there is no blame upon either of them concerning that by which she ransoms herself [i.e., with money given to obtain release from the marriage]." (Al-Baqarah 2:229), and by the hadith of the wife of Thabit ibn Qays. It is advisable to give the husband a chance, as he might amend his ways.