1. The problem states that the graph of the quadratic function $$y = 9x^2 + 9x - 4$$ is stretched horizontally by a factor of 5. 2. A horizontal stretch by a factor of 5 means every x-coordinate is replaced by $$\frac{x}{5}$$ in the function. 3. The new function after the horizontal stretch is obtained by substituting $$x$$ with $$\frac{x}{5}$$ in the original equation: $$y = 9\left(\frac{x}{5}\right)^2 + 9\left(\frac{x}{5}\right) - 4$$ 4. This is the equation of the new graph after the horizontal stretch. The problem states no simplification is needed. Final answer: $$y = 9\left(\frac{x}{5}\right)^2 + 9\left(\frac{x}{5}\right) - 4$$