what is the limit

[ 5n⁵ ] / [ 4n⁵ + 5 ]  

 

Dividing every term by n⁵   --->   [ 5n⁵ / nⁿ ] / [ 4n⁵ / n⁵  +  5 / n⁵ ]   =   5 / ( 4 + 5/n⁵ )

 

as n gets larger and larger, the term gets closer fand closer to  5/4  or 1.25

 

Adding an infinite set of numbers, each of whom is nearly 1.25, results in an answer that has no bound.