The ODE is separable:
[tex]3y\,\mathrm dx+(xy+5x)\,\mathrm dy=0\implies x(y+5)\,\mathrm dy=-3y\,\mathrm dx\implies\dfrac{y+5}y\mathrm dy=-\dfrac3x\,\mathrm dx[/tex]
Integrating both sides gives
[tex]\displaystyle\int\left(1+\frac5y\right)\,\mathrm dy=-3\int\frac{\mathrm dx}x\implies y+5\ln|y|=-3\ln|x|+C[/tex]
