To simplify the given expression, we need to divide the fraction \(\frac{5}{6}\) by 2. This can be done by multiplying \(\frac{5}{6}\) by the reciprocal of 2, which is \(\frac{1}{2}\). The result will be a new fraction.
Step 1: Define the Expression
We start with the expression to simplify:
\[
\frac{\frac{5}{6}}{2}
\]
Step 2: Rewrite the Division
To simplify the expression, we can rewrite the division by 2 as multiplication by its reciprocal:
\[
\frac{5}{6} \div 2 = \frac{5}{6} \times \frac{1}{2}
\]
Step 3: Perform the Multiplication
Now, we multiply the fractions:
\[
\frac{5}{6} \times \frac{1}{2} = \frac{5 \times 1}{6 \times 2} = \frac{5}{12}
\]
Final Answer
The simplified expression is
\[
\boxed{\frac{5}{12}}
\]