How would you find converge or diverges of an=5/n+2

This is what I did
Limit n--->∞ 5/∞+2=5/∞=0
So does it converge

it does converge to zero.

You can't formally use ∞ as a value.
You need to show that for sufficiently large n, an is less than any positive value, no matter how small.