To find the experimental probability that the next boat to dock will be from North Carolina, we can use the formula for experimental probability:
\[ P(\text{North Carolina}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}} \]
In this case, the number of favorable outcomes (boats from North Carolina) is 5, and the total number of trials (total boats that docked) is 13.
Thus, we calculate:
\[ P(\text{North Carolina}) = \frac{5}{13} \]
So, the experimental probability that the next boat to dock will be from North Carolina is:
\[ \frac{5}{13} \]