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This verse prohibits adultery.

Rashi on Deuteronomy 22:5 (c. 11th century)

"A woman should not put on the apparel of a man. . ." that she will resemble a man and go out amongst men for the purpose of adultery. "Nor should a man wear the clothing of a woman…" [Deuteronomy 22:5] in order to sit amongst the women. As we learned [in the Babylonian Talmud Nazir 59a]. "It is completely off-limits behavior…" [Therefore] the Torah is forbidding garments that lead to such off-limits behavior.

Further explanation on Rashi's comments.