Let's apply the rule to the given original point, which is (5, -1):
1. The rule states that each point is translated by 5 units to the right and 3 units down. In the rule, the first numerical value corresponds to the x-coordinate translation, and the second numerical value corresponds to the y-coordinate translation.
2. To determine the x-coordinate of the translated point, add the x-coordinate value from the rule (5) to the x-coordinate value of the original point (5), resulting in 10.
3. To determine the y-coordinate of the translated point, we need to subtract the y-coordinate value from the rule (-3) from the y-coordinate value of the original point (-1), giving us -1 - (-3) = -1 + 3 = 2.
4. Following these actions, our computed x and y coordinates of the new, translated point are (10, 2).
5. Now, we should compare our translated point to the options given. It matches option a. (10, 2).
So, the translated point after applying the rule (5, -3) to the original point (5, -1) is (10, 2). Hence, the answer to the question is 'a. (10, 2)'.
Answer: a. (10, 2)