What does "beyond 15 randomly selected. . ." mean? Does that mean someone asked 15 people and only 10 people recognized the brand? Not familiar with the wording.

If you assume that the population proportion is .95 recognize and .05 do not recognize, then this is a simple binomial distribution where you are calculating the probability of getting exactly 10 successes out of 15 tries. If you need help further than that, be sure to note where you are getting confused.