The general solution of $x{y}_5 = y_4$is given by 

$\begin{array}{l}x{y}_5=y_4\Rightarrow x\frac{d}{dx}{y}_4=y_4\\ \Rightarrow \frac{d{y}_4}{y_4}=\frac{dx}{x}\Rightarrow y_4=\left(\text{ Const }\right)x\end{array}$

so $y_3=\text{ const }{x}^2+\text{ const }$

$\begin{array}{l}\Rightarrow y_2=C_1^{\mathrm{\prime }}{x}^3+C_2^{\mathrm{\prime }}x+C_3^{\mathrm{\prime }}\\ \Rightarrow y_1=C_1^{\prime \prime }{x}^4+C_2^{\prime \prime }{x}^2+C_3^{\prime \prime }x+C_4^{\prime \prime }\\ \Rightarrow y=C_1{x}^5+C_2{x}^3+C_3{x}^2+C_{4}x+C_5.\end{array}$