First, let's multiply out (a-3b)(a+2b):

(a-3b)(a+2b) = a(a) + a(2b) - 3b(a) - 3b(2b)
= a^2 + 2ab - 3ab - 6b^2
= a^2 - ab - 6b^2

Next, let's multiply out 5a(a+2b):

5a(a+2b) = 5a(a) + 5a(2b)
= 5a^2 + 10ab

Now, let's add the two results together:

(a^2 - ab - 6b^2) + (5a^2 + 10ab)
= a^2 + 5a^2 - ab + 10ab - 6b^2
= 6a^2 + 9ab - 6b^2

Therefore, the final result is 6a^2 + 9ab - 6b^2.