If All the Solution Curves For $\frac { d y } { d t }$

True/False

If all the solution curves for $\frac { d y } { d t }$ have $y = - 5$ as a horizontal asymptote, does it follow that either $\lim _ { t \rightarrow \infty } y = 5$ or $\lim _ { t \rightarrow - \infty } y = 5$ ?