If the probability of Tiffany pulling out a white pair of shoes is \( \frac{2}{5} \), this means that the remaining probability must account for the black shoes. Since the total probability must equal 1, we can calculate the probability of pulling out a black pair of shoes as follows:
\[ P(\text{black shoes}) = 1 - P(\text{white shoes}) = 1 - \frac{2}{5} \]
Calculating this:
\[ P(\text{black shoes}) = 1 - \frac{2}{5} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5} \]
Therefore, the chance of Tiffany randomly pulling out a black pair of shoes is \( \frac{3}{5} \).