Answer
$\color{blue}{\dfrac{13\sqrt[3]{4}}{6}}$
Work Step by Step
Simplify the denominators to obtain:
$=\dfrac{5}{\sqrt[3]{2}} - \dfrac{2}{\sqrt[3]{8(2)}} + \dfrac{1}{\sqrt[3]{27(2)}}
\\=\dfrac{5}{\sqrt[3]{2}} - \dfrac{2}{2\sqrt[3]{2}}+ \dfrac{1}{3\sqrt[3]{2}}$
Make the expressions similar by using their LCD of $6\sqrt[3]{2}$ to obtain:
$=\dfrac{5(6)}{\sqrt[3]{2}(6)}- \dfrac{2(3)}{2\sqrt[3]{2}(3)}+\dfrac{1(2)}{3\sqrt[3]{2}(2)}
\\=\dfrac{30}{6\sqrt[3]{2}}-\dfrac{6}{6\sqrt[3]{2}}+\dfrac{2}{6\sqrt[3]{2}}$
Perform the operations to the numerators and copy the denominator to obtain:
$=\dfrac{30-6+2}{6\sqrt[3]{2}}
\\=\dfrac{26}{6\sqrt[3]{2}}$
Rationalize the denominator by multiplying $\sqrt[3]{4}$ to both the numerator and the denominator to obtain:
$=\dfrac{26(\sqrt[3]{4})}{6\sqrt[3]{2}(\sqrt[3]{4})}
\\=\dfrac{26\sqrt[3]{4}}{6(\sqrt[3]{8})}
\\=\dfrac{26\sqrt[3]{4}}{6(2)}
\\=\dfrac{26\sqrt[3]{4}}{12}$
Cancel the common factor $2$ to obtain:
$\require{cancel}=\dfrac{\cancel{26}^{13}\sqrt[3]{4}}{\cancel{12}6}
\\=\color{blue}{\dfrac{13\sqrt[3]{4}}{6}}$
