The total number of bulbs in the box is 100, out of which 10 are defective. We need to find the probability that out of a sample of 5 bulbs, none is defective.

To solve this problem, we can use the concept of combinations. The number of ways to choose 5 bulbs out of 100 is given by the combination formula:

C(100, 5) = 100! / (5!(100-5)!) = 75,287,520

Now, let's consider the favorable outcomes, i.e., the number of ways to choose 5 bulbs that are not defective. Since there are 10 defective bulbs, there are 90 bulbs that are not defective. The number of ways to choose 5 non-defective bulbs out of 90 is given by:

C(90, 5) = 90! / (5!(90-5)!) = 75,287,520

Therefore, the probability of choosing 5 non-defective bulbs out of 100 is:

P = C(90, 5) / C(100, 5) = 75,287,520 / 75,287,520 = 1

This means that the probability of choosing 5 non-defective bulbs out of 100 is 1, or 100%. However, this cannot be the correct answer because it is not one of the given options.

Let's reconsider the problem. We need to find the probability that out of a sample of 5 bulbs, none is defective. This can be achieved by choosing all 5 bulbs from the set of non-defective bulbs. The probability of choosing a non-defective bulb is 90/100 = 9/10. Since we want to choose 5 non-defective bulbs, the probability is given by:

P = (9/10)^5 = 9^5 / 10^5 = 59049 / 100000

Simplifying this fraction, we get:

P = 0.59049

Therefore, the probability that out of a sample of 5 bulbs, none is defective is 0.59049, which is approximately equal to 0.59. This corresponds to option B, (9/10)^5, which is the correct answer.