1. **Problem:** Find the equation of a line with gradient 5 passing through the point $(-1, -3)$. 2. **Formula:** The equation of a line with gradient $m$ passing through point $(x_1, y_1)$ is given by the point-slope form: $$y - y_1 = m(x - x_1)$$ 3. **Substitute values:** Here, $m=5$, $x_1 = -1$, and $y_1 = -3$. So, $$y - (-3) = 5(x - (-1))$$ 4. **Simplify:** $$y + 3 = 5(x + 1)$$ 5. **Distribute:** $$y + 3 = 5x + 5$$ 6. **Isolate $y$:** $$y = 5x + 5 - 3$$ 7. **Simplify:** $$y = 5x + 2$$ **Final answer:** The equation of the line is $$y = 5x + 2$$