Is Absolute Convergence Possible for \sum_{n=1}^{\infty}(-1)^n\frac{n}{5+n}?

[nameVoid]

$$\sum_{n=1}^{\infty}(-1)^n\frac{n}{5+n}$$
alt series tests fails, ratio and root fail is it safe to do a comp test with bn=1 for c=1>0 for abs convergence

 

[nameVoid]

the answer here is no since the limit of an does not approach 0