The key to solving this problem is to know that parallel lines have the same slope. So, the equation of the line we're looking for can be written as y = 5x + b, because it's the same slope, 5, as the line y = 5x + 2.
The 'b' represents the y-intercept of the line, and it's the only thing we don't know yet.
To find 'b', we can use the fact that the line passes through the point (-2, 2). This means that when x = -2, y = 2. We substitute these values into the equation, giving us 2 = 5 * -2 + b.
Solve the equation for b, which is:
b = 2 - 5 * -2.
Remember to multiply first (PMDAS/BODMAS rule), giving us b = 2 + 10,
Therefore, b = 12.
In conclusion, the equation of the line parallel to y = 5x + 2, which passes through the point (-2, 2), is y = 5x + 12.