$\text{a)}\frac{1}{2}\sqrt[3]{-1}+\frac{1}{3}\sqrt[5]{-32}=\frac{1}{2}\cdot \left(-1\right)+\frac{1}{3}\cdot \left(-2\right)=-\frac{1}{2}-\frac{2}{3}=-\frac{3}{6}-\frac{4}{6}=-\frac{7}{6}=-1\frac{1}{6}$  

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$\text{b)}3\sqrt[3]{-0,125}-2\sqrt[3]{-125}=3\sqrt[3]{-\frac{1}{8}}-2\cdot \left(-5\right)=3\cdot \left(-\frac{1}{2}\right)+10=-\frac{3}{2}+10=$  

$=-1,5+10=8,5$  

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$\text{c)}3\sqrt[3]{-0,008}\cdot \sqrt[5]{-0,00032}=3\cdot \left(-0,2\right)\cdot \left(-0,2\right)=3\cdot 0,04=0,12$  

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$\text{d)}\sqrt[3]{-2}\cdot \sqrt[3]{-500}=\sqrt[3]{-2\cdot \left(-500\right)}=\sqrt[3]{1000}=10$  

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$\text{e)}\sqrt[3]{-56}:\sqrt[3]{7}=\sqrt[3]{-56:7}=\sqrt[3]{-8}=-2$  

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$\text{f)}\sqrt[3]{-15}:\sqrt[3]{-120}=\sqrt[3]{\frac{-15}{-120}}=\sqrt[3]{\frac{15}{120}}=\sqrt[3]{\frac{1}{8}}=\frac{1}{2}$