To determine the value of \( k \) in the function \( g(y) = y + k \) that describes the translation of the point from \( (5, -3) \) to \( (5, 7) \), we need to analyze how the \( y \)-coordinate changes during the translation.
The initial \( y \)-coordinate is \( -3 \), and after the translation, the \( y \)-coordinate is \( 7 \).
This means:
\[ g(-3) = 7 \]
Substituting \(-3\) into the function:
\[ -3 + k = 7 \]
To solve for \( k \), we rearrange the equation:
\[ k = 7 + 3 \] \[ k = 10 \]
Thus, the value of \( k \) is \( \boxed{10} \).
This means the function that describes the translation is \( g(y) = y + 10 \).