Answer: Series diverges to infinity
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Explanation:
The leading terms of the numerator and denominator are 5n^5 and 4n^5 respectively. They divide to 5/4. The n^5 portions cancel.
As n approaches infinity, the nth term of the sequence is going to approach 5/4 = 1.25 which is larger than 1.
Adding stuff to a series that's larger than 1, and doing so infinitely many times, means that the partial sums explode to infinity. The partial sums do not approach a finite value. Therefore, this series diverges to infinity.
