1. **State the problem:** Find the points of intersection between the quadratic function $$y = x^2 - 5x - 2$$ and the linear function $$y = -x + 3$$. 2. **Set the equations equal to find intersection points:** Since both expressions equal $$y$$, set them equal: $$x^2 - 5x - 2 = -x + 3$$ 3. **Bring all terms to one side to form a quadratic equation:** $$x^2 - 5x - 2 + x - 3 = 0$$ $$x^2 - 4x - 5 = 0$$ 4. **Factor the quadratic equation:** $$x^2 - 4x - 5 = (x - 5)(x + 1) = 0$$ 5. **Solve for $$x$$:** $$x - 5 = 0 \Rightarrow x = 5$$ $$x + 1 = 0 \Rightarrow x = -1$$ 6. **Find corresponding $$y$$ values by substituting $$x$$ into one of the original equations, e.g., $$y = -x + 3$$:** For $$x = 5$$: $$y = -5 + 3 = -2$$ For $$x = -1$$: $$y = -(-1) + 3 = 1 + 3 = 4$$ 7. **Final answer:** The points of intersection are $$\boxed{(5, -2)}$$ and $$\boxed{(-1, 4)}$$.