5. Упростите выражение: (−3/√5)² + (2√2)²/15 − √125/√5 + (2√2/√3)².

Упростим каждый член:

\(\left(-\frac{3}{\sqrt{5}}\right)^2=\frac{9}{5}\), \(\frac{(2\sqrt{2})^2}{15}=\frac{8}{15}\), \(\frac{\sqrt{125}}{\sqrt{5}}=\sqrt{25}=5\), \(\left(\frac{2\sqrt{2}}{\sqrt{3}}\right)^2=\frac{8}{3}\).

\(\frac{9}{5}+\frac{8}{15}-5+\frac{8}{3}=\frac{27}{15}+\frac{8}{15}-\frac{75}{15}+\frac{40}{15}=0\).

Ответ: \(0\)