Use Chebyshev's theorem to solve the problem.

Find the least possible fraction of numbers in a data set lying within 5 standard deviations of the mean.
$\frac{4}{5}$
$\frac{24}{25}$
$\frac{1}{5}$
$\frac{1}{25}$

Step 1 ：Given a math problem, we are asked to find the least possible fraction of numbers in a data set lying within 5 standard deviations of the mean.

Step 2 ：We can use Chebyshev's theorem to solve this problem. Chebyshev's theorem states that at least 1 - 1/k^2 of the data from a distribution will fall within k standard deviations of the mean, for all k > 1.

Step 3 ：In this case, we substitute k = 5 into the formula and calculate the fraction.

Step 4 ：The calculation is as follows: 1 - 1/(5^2) = 1 - 1/25 = 24/25 = 0.96

Step 5 ：So, the least possible fraction of numbers in a data set lying within 5 standard deviations of the mean is \( \boxed{\frac{24}{25}} \) or 0.96.