Step 1 :Given a point (2, -4) and a slope -5, we can use the point-slope form of a line equation which is given by \(y - y_1 = m(x - x_1)\).
Step 2 :Substitute the given values into the formula, we get \(y - -4 = -5(x - 2)\).
Step 3 :Simplify the equation to get the final answer: \(\boxed{y + 4 = -5(x - 2)}\).