To determine the time taken for seven-eighths of a sample to decay, we need to consider the concept of half-life.

Half-life is defined as the time it takes for half of a radioactive substance to decay. In this case, the substance B210 has a half-life of 5 days.

To find the time taken for seven-eighths of the sample to decay, we can use the following steps:

1. Determine the number of half-lives required for seven-eighths of the sample to decay:
- Since each half-life reduces the sample by half, we need to find how many times we need to halve the sample to reach seven-eighths remaining.
- To do this, we can calculate the fraction of the sample remaining after each half-life until we reach seven-eighths.
- After the first half-life, half of the sample remains (1/2).
- After the second half-life, one-fourth of the sample remains (1/2 * 1/2 = 1/4).
- After the third half-life, one-eighth of the sample remains (1/2 * 1/2 * 1/2 = 1/8).
- After the fourth half-life, one-sixteenth of the sample remains (1/2 * 1/2 * 1/2 * 1/2 = 1/16).
- After the fifth half-life, one-thirty-second of the sample remains (1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32).
- After the sixth half-life, one-sixty-fourth of the sample remains (1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64).
- After the seventh half-life, one-hundred-twenty-eighth of the sample remains (1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/128).
- At this point, we have reached seven-eighths of the sample remaining (1 - 1/128 = 127/128).

2. Calculate the time taken for seven-eighths of the sample to decay:
- Since each half-life is 5 days, we need to multiply the number of half-lives by 5 to find the total time taken.
- In this case, we have reached seven-eighths of the sample after 7 half-lives (5 days * 7 = 35 days).

Therefore, the correct answer is option D) 15 days.