[tex]25^{x+2}=125^{x+5}\\(5^{2})^{x+2}=(5^{3})^{x+5}\\\not{5}^{2x+4}=\not{5}^{3x+15}\\2x+4=3x+15\\-x=11~\bullet(-1)\\\boxed{x=-11}[/tex]
[tex] \sqrt[3]{25^{x}} = \sqrt{5} \\ \sqrt[3]{(5^{2})^{x}} = \sqrt{5} \\ \sqrt[3]{5^{2x}} = \sqrt{5} \\\not{5}^{ \frac{2x}{3} }=\not{5}^{ \frac{1}{2} }[/tex]
[tex] \frac{2x}{3} = \frac{1}{2} ~~4x=3~~\boxed{x= \frac{3}{4} }[/tex]
