5. We will call a number $\mathrm{X}$ "25-supporting" if for any 25 real numbers $a_{1}, \ldots, a_{25}$, the sum of which is an integer, there exists at least one for which $\left|a_{i}-\frac{1}{2}\right| \geq X$.

In your answer, specify the largest 25-supporting X, rounded to the hundredths according to standard mathematical rules.
Answer $\frac{1}{50}=\mathbf{0 . 0 2}$.