To find out how many barrels of tomatoes the farmers picked on Thursday, we start with the amount they picked on Wednesday, which is 99 barrels.
On Thursday, the farmers picked \( \frac{1}{5} \) as many tomatoes as on Wednesday. To calculate this, we multiply the number of barrels picked on Wednesday by \( \frac{1}{5} \):
\[ \text{Tomatoes picked on Thursday} = \frac{1}{5} \times 99 \]
Now, we can perform the multiplication:
\[ \frac{1}{5} \times 99 = \frac{99}{5} \]
To express \( \frac{99}{5} \) as a mixed number, we divide 99 by 5:
- 5 goes into 99 a total of 19 times, since \( 5 \times 19 = 95 \).
- The remainder is \( 99 - 95 = 4 \).
Thus, we can write:
\[ \frac{99}{5} = 19 \frac{4}{5} \]
Therefore, the farmers picked
\[ \boxed{19 \frac{4}{5}} \]
barrels of tomatoes on Thursday.