The new mean is $\mu_{\text{new}} = 79$.

The new mean is $\mu_{\text{new}} = 74$ because adding a constant does not shift the center.

The new mean satisfies the relation $\mu_{\text{new}} = \mu + 5$.

The sum of the new scores is $5N$ greater than the sum of the original scores, where $N$ is the number of scores.