5/6+5/2*2/3

Let's simplify the expression step by step:

\[ \frac{5}{6} + \frac{5}{2} \times \frac{2}{3} \]

First, handle the multiplication:

\[ \frac{5}{2} \times \frac{2}{3} = \frac{5 \times 2}{2 \times 3} = \frac{10}{6} = \frac{5}{3} \]

Now, add \(\frac{5}{6}\) to \(\frac{5}{3}\):

To add these fractions, find a common denominator, which is 6:

\[ \frac{5}{6} + \frac{5}{3} = \frac{5}{6} + \frac{5 \times 2}{3 \times 2} = \frac{5}{6} + \frac{10}{6} = \frac{5 + 10}{6} = \frac{15}{6} \]

Simplify \(\frac{15}{6}\):

\[ \frac{15}{6} = \frac{15 \div 3}{6 \div 3} = \frac{5}{2} \]

Final answer:

\[ \boxed{\frac{5}{2}} \]