double check answer?

Correct, Jenny   !!!!

Here's a way to see this

Divide each term by  n^4    and we get that

             3n^5 / n^4

______________________  = 

15n^4 / n^4    +    5/n^4

            3n

_______________        if we let  n  approachi infinity,  5/n^4   approaches    0

    15     +  5/n^4

So    we are left with

(3/15)n

And  as n approches infinity  this term also  approacnes infinity.....so.....the series does not  resolve to any specific value