The point-slope form of a line is given by the equation:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope, and \((x_1, y_1)\) is a point on the line.
In this case, the slope \( m \) is 5, and the point is \((3, -4)\). Plugging these values into the point-slope form, we have:
\[ y - (-4) = 5(x - 3) \]
This simplifies to:
\[ y + 4 = 5(x - 3) \]
Thus, the point-slope form of the line is:
\[ y + 4 = 5(x - 3) \]