(5/4-5/6)•3/5

To solve the expression \((\frac{5}{4} - \frac{5}{6}) \cdot \frac{3}{5}\), we first need to find a common denominator for the fractions \(\frac{5}{4}\) and \(\frac{5}{6}\).

The least common multiple (LCM) of 4 and 6 is 12.

Now, we convert both fractions:

\[ \frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12} \]

\[ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \]

Now, we can subtract the two fractions:

\[ \frac{15}{12} - \frac{10}{12} = \frac{15 - 10}{12} = \frac{5}{12} \]

Next, we multiply this result by \(\frac{3}{5}\):

\[ \left(\frac{5}{12}\right) \cdot \left(\frac{3}{5}\right) = \frac{5 \times 3}{12 \times 5} = \frac{15}{60} \]

Now, we can simplify \(\frac{15}{60}\):

\[ \frac{15 \div 15}{60 \div 15} = \frac{1}{4} \]

So, the final result is:

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