To find out how many hours Oscar spent watching television, we start with the number of hours Florence watched, which is 2 hours.
Oscar watched television for \( \frac{1}{5} \) of the hours Florence did. Thus, we calculate Oscar's viewing time as follows:
\[ \text{Oscar's hours} = \frac{1}{5} \times 2 \]
Now, we perform the multiplication:
\[ \frac{1}{5} \times 2 = \frac{2}{5} \]
Therefore, Oscar spent \( \frac{2}{5} \) hours watching television.
Thus, the final answer is \( \frac{2}{5} \).