To find an equation of a line perpendicular to $y = -5x - 2$ and passing through the point $(-10, -5)$, we need to follow these steps:

1. Find the slope of the given line: The equation of the given line is $y = -5x - 2$. The slope of this line is $-5$.

2. Determine the slope of the perpendicular line: The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line is: $m = -\frac{1}{-5} = \frac{1}{5}$

3. Use the point-slope form of the line equation: The point-slope form of the equation of a line is given by: $y - y_1 = m(x - x_1)$ Here, $m = \frac{1}{5}$ and the point $(x_1, y_1) = (-10, -5)$.

4. Substitute the slope and the point into the point-slope form: $y - (-5) = \frac{1}{5}(x - (-10))$ Simplify this equation: $y + 5 = \frac{1}{5}(x + 10)$

5. Distribute and solve for $y$: $y + 5 = \frac{1}{5}x + 2$ $y = \frac{1}{5}x + 2 - 5$ $y = \frac{1}{5}x - 3$

Therefore, the equation of the line perpendicular to $y = -5x - 2$ and passing through the point $(-10, -5)$ is: $y = \frac{1}{5}x - 3$

Would you like more details or have any questions?

Here are 5 questions you can ask next:

1. How do you find the equation of a line given two points?
2. What is the distance formula between two points in a plane?
3. How do you find the midpoint of a line segment?
4. What is the general form of the equation of a circle?
5. How do you convert a quadratic equation from standard form to vertex form?

Tip: When working with linear equations, always remember that perpendicular lines have slopes that are negative reciprocals of each other.