To simplify the expression:

First, divide 3a^n+5 by 44a^2:
(3a^n + 5) / (44a^2)
= (3a^n / 44a^2) + (5 / 44a^2)
= 3/44 (a^n-2) + 5/44a^2

Next, divide a^n-5 by 22a:
(a^n - 5) / (22a)
= a^n / 22a - 5 / 22a
= 1/22 (a^n-1) - 5/22a

Therefore, the simplified expression is:
(3/44(a^n-2) + 5/44a^2) : (1/22(a^n-1) - 5/22a)