please help!!! i'll give brainliest

Answer:
Does not exist
Step-by-step explanation:
[tex]\sum _{n=1}^{\infty \:}(\frac{5n^5}{4n^5+5})[/tex]
Apply the divergence test.
[tex]\lim_{n \to \infty} (\frac{5n^{5}}{4n^{5}+5})[/tex]
⇒ diverges
If an infinite series is a divergent sequence, it has no limit.
~Hope this helps!~
(Yes I did answer twice since you asked the question twice :P)