Answer
$\color{blue}{\dfrac{5}{x^2}}$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$
(4) $(ab)^m = a^mb^m$
(5) $(a^m)^n=a^{mn}$
(6) $a^m \cdot a^n = a^{m+n}$
(7) $a^0=1, a\ne0$
Use rule (4) above to obtain:
$=\dfrac{(5^{-2}x^{-2}) \cdot 5^{-3}(x^3)^{-3}}{(5^{-2})^{3}(x^{-3})^3}$
Use rule (5) above to obtain:
$=\dfrac{5^{-2}x^{-2}\cdot 5^{-3}(x^{3(-3)})}{5^{-3(2)}x^{-3(3)}}
\\=\dfrac{5^{-2}x^{-2} \cdot 5^{-3}x^{-9}}{5^{-6}x^{-9}}$
Use rule (6) above to obtain:
$=\dfrac{5^{-2+(-3)}x^{-2+(-9)}}{5^{-6}x^{-9}}
\\=\dfrac{5^{-5}x^{-11}}{5^{-6}x^{-9}}$
Use rule (2) above to obtain:
$=5^{-5-(-6)}x^{-11-(-9)}
\\=5^{-5+6}x^{-11+9}
\\=5^1x^{-2}
\\=5x^{-2}$
Use rule (1) above to obtain:
$=5 \cdot \dfrac{1}{x^2}
\\=\color{blue}{\dfrac{5}{x^2}}$
