In a parallelogram, opposite sides are equal in length. Given that \( BC = 7 , \text{cm} \) and \( CD = 5 , \text{cm} \), we can determine the lengths of the sides \( AB \) and \( AD \).
Since \( AB \) is opposite to \( BC \), it follows that: \[ AB = BC = 7 , \text{cm} \]
Additionally, since \( AD \) is opposite to \( CD \), it follows that: \[ AD = CD = 5 , \text{cm} \]
Thus, the length of \( AB \) is \( 7 , \text{cm} \).
So the correct answer is: 7 cm