Let's add up the given scores to get: 97+38+88+75+83 = 381. Then we divide by 5 since there are five scores here. The mean we get is 381/5 = 76.2
So that explains the "76.2" mentioned.
Now we'll replace the "38" with "58" and repeat the same steps as above.
Add: 97+58+88+75+83 = 401
Divide by five: 401/5 = 80.2
The mean is now 80.2; it has increased compared to the previous mean. We can see that if we move any outliers closer to the main cluster, then the mean will be centered more around the main cluster. In the other direction, if we move the outlier further away from the cluster, then the outlier pulls on the mean. Think of a magnetic or gravitational pull.
The smaller outlier 38 made the mean of 76.2 to be smaller than it should be if we focused on the other values only. In short, if your data set has outliers, then the mean may likely not reflect the true center average value of the group. At that point, the median may be the next best thing or you could use a trimmed mean.