If y=y(x) is the solution of the differential

$\frac{\left(5+\mathrm{e}^{\mathrm{x}}\right)}{2+\mathrm{y}} \frac{\mathrm{dy}}{\mathrm{dx}}=-\mathrm{e}^{\mathrm{x}}$

$\int \frac{d y}{2+y}=\int \frac{-e^{x}}{e^{x}+5} d x$

$\ln (y+2)=-\ln \left(e^{x}+5\right)+k$

$(y+2)\left(e^{x}+5\right)=C$

$\because y(0)=1$

$\Rightarrow \mathrm{C}=18$

$y+2=\frac{18}{e^{x}+5}$

at $x=\ln 13$

$y+2=\frac{18}{13+5}=1$

$y=-1$