Answer
$x^2\sqrt[6]{x}$
Work Step by Step
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ then
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{x^5}}{\sqrt[3]{x}}
\\\\=
\dfrac{x^{5/2}}{x^{1/3}}
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^{5/2}}{x^{1/3}}
\\\\=
x^{\frac{5}{2}-\frac{1}{3}}
\\\\=
x^{\frac{15}{6}-\frac{2}{6}}
\\\\=
x^{\frac{13}{6}}
.\end{array}
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ then
\begin{array}{l}\require{cancel}
x^{\frac{13}{6}}
\\\\=
\sqrt[6]{x^{13}}
.\end{array}
Extracting the factor that is a perfect power of the index, then
\begin{array}{l}\require{cancel}
\sqrt[6]{x^{13}}
\\\\=
\sqrt[6]{x^{12}\cdot x}
\\\\=
\sqrt[6]{(x^{2})^6\cdot x}
\\\\=
x^2\sqrt[6]{x}
.\end{array}