To find the value of \( k \) in the function \( g(y) = y + k \) that describes the translation of the point \( (5, -3) \) to \( (5, 7) \), we can observe the change in the \( y \)-coordinates.
The initial \( y \)-coordinate is \( -3 \) and the final \( y \)-coordinate is \( 7 \).
The translation can be described by the change in \( y \):
\[ \text{Change in } y = 7 - (-3) = 7 + 3 = 10 \]
Thus, the function \( g(y) \) that describes this translation will be:
\[ g(y) = y + 10 \]
This means \( k = 10 \).
Therefore, the value of \( k \) is \( \text{b. } 10 \).