$$\left({\left(\frac{5x^{-5}}{2y^{-2}}\right)}^{-2}·{\left(\frac{y^{-1}}{5x^{-1}}\right)}^{-3}\right)÷10x^2{y}^{-3}$$

$$=\left({\left(\frac{5y^2}{2x^5}\right)}^{-2}·{\left(\frac{x}{5y}\right)}^{-3}\right)÷10x^2{y}^{-3}$$

$$=\left({\left(\frac{2x^5}{5y^2}\right)}^2·{\left(\frac{5y}{x}\right)}^3\right)÷10x^2\frac{1}{y^3}$$

$$=\left(\left(\frac{2^2{x}^{5·2}}{5^2{y}^{2·2}}\right)·\left(\frac{5^3{y}^3}{x^3}\right)\right)÷\frac{10x^2}{y^3}$$

$$=\left(\frac{4x^{10}}{25y^4}·\frac{125y^3}{x^3}\right)÷\frac{10x^2}{y^3}$$

$$=\left(\frac{4\bcancel{x^{10}}}{\cancel{25y^4}}·\frac{\cancel{125y^3}}{\bcancel{x^3}}\right)÷\frac{10x^2}{y^3}$$

$$=\left(\frac{4x^7}{1}·\frac{5}{1}\right)÷\frac{10x^2}{y^3}$$

$$=20x^7÷\frac{10x^2}{y^3}$$

$$=\frac{\bcancel{20x^7}}{1}·\frac{y^3}{\bcancel{10x^2}}$$