To find the points of intersection between the line y = -5 and the circle defined by (x-3)² + (y+2)² = 25, substitute y = -5 into the circle's equation. This leads to the equation (x-3)² + (-5+2)² = 25, simplifying to (x-3)² + 9 = 25. Further simplification gives (x-3)² = 16, allowing for the solution of x values. The resulting x values are x = 7 and x = -1, indicating that the line intersects the circle at two points: (7, -5) and (-1, -5). Thus, the line intersects the circle at two distinct points.