To find the value of \( c \) such that the graph of the equation \( 3x + c = 5y \) has an x-intercept of \( (-4, 0) \), we can substitute the x-intercept coordinates into the equation.
The x-intercept is the point where the graph crosses the x-axis, meaning \( y = 0 \). Therefore, we substitute \( y = 0 \) and \( x = -4 \) into the equation:
\[ 3(-4) + c = 5(0) \]
This simplifies to:
\[ -12 + c = 0 \]
To solve for \( c \), we add 12 to both sides:
\[ c = 12 \]
Thus, the value of \( c \) is \( \boxed{12} \).