Probably this precept was meant to distinguish GOD'S people from their idolatrous neighbours, among whom, and probably for the gratification of their lusts, the distinction of the sex in their dress was not preserved. And it is possible, it might have a further object of a religious and spiritual nature. The apostle seems to have the same idea in view, when he speaks of the different dresses of the sexes in his Epistle to the Corinthians. 1 Corinthians 11:12-13.
Related Commentaries of Deuteronomy 22:5
Deuteronomy 22:5
5 The woman shall not wear that which pertaineth unto a man, neither shall a man put on a woman's garment: for all that do so are abomination unto the LORD thy God.