\(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\frac{\left(-10\right)^5}{\left(-3\right)^5}.\frac{\left(-6\right)^4}{\left(-5\right)^4}=\frac{\left(-5\right)^4.\left(-5\right).\left(-2\right)^5}{\left(-3\right)^4.\left(-3\right)}.\frac{\left(-3\right)^4.\left(-2\right)^4}{\left(-5\right)^4}=\frac{\left(-5\right).\left(-2\right)^5.\left(-2\right)^4}{\left(-3\right)}\)
\(=\frac{\left(-5\right).\left(-2\right)^9}{\left(-3\right)}\)