The expression $-\left(\frac{5}{2}\right)^3$ can be simplified as follows:

1. First, calculate the cube of $\frac{5}{2}$: $\left(\frac{5}{2}\right)^3 = \frac{5^3}{2^3} = \frac{125}{8}$

2. Then, apply the negative sign to the result: $-\frac{125}{8}$

So, the simplified result is $-\frac{125}{8}$.

Would you like more details or have any questions?

Here are five related questions:

1. What is the value of $\left(\frac{3}{4}\right)^2$?
2. How do you simplify $-\left(\frac{7}{3}\right)^2$?
3. What is $\left(\frac{2}{5}\right)^3$?
4. How do you solve $-\left(\frac{9}{4}\right)^3$?
5. What is the result of $\left(-\frac{3}{2}\right)^2$?

Tip: When raising a fraction to a power, remember to apply the exponent to both the numerator and the denominator.