Create the "hole" at x= 5 by introducing a factor of (x-5) in both numerator and denominator of rational function.
Do create a vertical asymptote at x=-6, introduce a factor of (x+6) in the denominator.
In order to have a horizontal asymptote at y=7 the reduced function (after the (x-5) factors are cancelled) must approach 7 as x->∞ (or -∞). An example of that would be y = 7x/(x+6), or (7x-3)/(x+6), etc.
See the above graph for an example.