Yesterday, Paula's Doughnut Shop sold 1/5 as many chocolate doughnuts as cinnamon doughnuts. If they sold 1/4 of a tray of cinnamon doughnuts, how many trays of chocolate doughnuts did they sell?

Let the number of trays of cinnamon doughnuts sold be \( x \). According to the problem, they sold \( \frac{1}{4} \) of a tray of cinnamon doughnuts. Therefore, we have:

\[ x = \frac{1}{4} \]

Now, according to the information given, Paula's Doughnut Shop sold \( \frac{1}{5} \) as many chocolate doughnuts as they sold cinnamon doughnuts.

To find the number of trays of chocolate doughnuts sold, we compute:

\[ \text{Trays of chocolate doughnuts} = \frac{1}{5} \times x \]

Substituting \( x = \frac{1}{4} \) into this equation gives:

\[ \text{Trays of chocolate doughnuts} = \frac{1}{5} \times \frac{1}{4} \]

To multiply the fractions, we multiply the numerators and the denominators:

\[ = \frac{1 \times 1}{5 \times 4} = \frac{1}{20} \]

Thus, the number of trays of chocolate doughnuts sold is:

\[ \boxed{\frac{1}{20}} \]