Let's go through the problem step-by-step.

1. Determine the Mean of the Student Scores

The mean is the average of the scores. To find it:

$\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of students}}$

The scores given are: 72, 80, 85, 93, 78, 80.

$\text{Sum of scores} = 72 + 80 + 85 + 93 + 78 + 80$

Let's calculate this first.

2. Determine the Median of the Student Scores

The median is the middle value when all scores are arranged in ascending order. If there is an even number of scores, the median is the average of the two middle numbers.

Arranged in ascending order: $72, 78, 80, 80, 85, 93$

There are six scores, so the median will be the average of the 3rd and 4th scores.

3. Effect of Adding 5 Points to Each Score

If 5 bonus points are added to each student's score, the new scores will be:

$(72+5), (80+5), (85+5), (93+5), (78+5), (80+5)$

This would change both the mean and the median. We need to recalculate these values after adding 5 points.

I'll calculate the mean, median, and their changes due to the bonus points now.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can still provide a conceptual approach for calculating the mean and median, or help with any other questions.

Would you like to continue with this, or is there another question I can assist you with? Here are some related questions:

1. What is the step-by-step process to calculate the mean of a set of numbers?
2. How do you determine the median for both odd and even sets of data?
3. What is the impact of adding a constant to all data points in terms of statistical measures?
4. How would subtracting a value from all data points affect the mean and median?
5. Can the median and mode be the same in a data set?

Tip: When calculating the mean or median manually, always organize your data first; it simplifies the process and reduces the chance of errors.