Problem #$3$: Given the autonomous differential equation

$y^{\text{'}}=(y-5)(y-8{)}^{2}ln(y+6)$

$($a$)$ For which of the initial conditions given below does $\underset{t}{lim}y(t)=-5$

$($b$)$ What sort of equilibrium is $y=5$ for our differential equation?

$($A$)$ Both $y(4)=0,y(1)=-\frac{17}{3}$

$($B$)y(4)=0$

$($C$)$ Neither $y(4)=0,y(1)=-\frac{17}{3}$

$($D$)y(1)=-\frac{17}{3}$