$-\frac{1}{2}\cdot \frac{5}{7}$

Step 1 ：Given the two fractions $-\frac{1}{2}$ and $\frac{5}{7}$, we are asked to find the product of these two fractions.

Step 2 ：The rule for multiplying fractions is to multiply the numerators (the top numbers) to get the new numerator, and multiply the denominators (the bottom numbers) to get the new denominator.

Step 3 ：Multiplying the numerators, we get $-1\times 5=-5$.

Step 4 ：Multiplying the denominators, we get $2\times 7=14$.

Step 5 ：So, the product of the two fractions is $-\frac{5}{14}$.

Step 6 ：Converting this fraction to a decimal, we get $-0.35714285714285715$.

Step 7 ：Final Answer: The result of the multiplication of the two fractions $-\frac{1}{2}\cdot \frac{5}{7}$ is $\boxed{{\displaystyle -0.35714285714285715}}$.