Find the quotient and any excluded values.(x + 5/x^2 + 9x + 20)/(x^2-16/x-4)

By  (x + 5/x^2 + 9x + 20) you apparently meant the following:

         x+5
 ----------------------
   x^2 + 9x + 20

and by 

(x^2-16/x-4)
                                       x^2-16
you apparently meant ---------------
                                         x - 4

Please use additional parentheses for clarity.

Dividing,

         x+5                   (x-4)(x+4)
 ----------------------  *  ---------------
   x^2 + 9x + 20                  x-4

Now, x^2 + 9x + 20 factors into   (x+4)(x+5), so what we have now is

       (x+5)(x+4)
------------------------- = 1           This is true for all x, so there are no exclusions.
    (x+4)(x+5)