Well you can use the Theorem that says you can treat the function a(n) as a function of x to help determine the limit so
The limit as
Similarly by properties of limits we can do
The limit as for

separately
The limit of 5 is obviously just 5 because it is constant and then the limit of the second portion is as such
which then each indiviual limit is taking your whole limit is equal to
which is obviously 0
then you can combined the to which is again...obviously the limit of 5 which is 5
Hope I did this right or I feel incredible dumb, I don't if i used the definition properly by the terms discussed above